The back of my samsung RF261BEAEBC/AA is leaking at the water line connection to the support water pipe fixture

Are you dealing with a plumbing emergency like a leaking water heater, a sewer that's backing up, burst pipes, blocked drains, an overflowing toilet, or a washing machine that has a water supply line that's leaking? Sounds like an urgent situation. You would be best to call a plumber asap.
For more info this might help: https://3pointsplumbing.ca/services/leaks.html

Look at the piping to each fixture. If they are flexible lines you can easily swap them after turning off the water supply. The fixtures themselves are the same so that is not a problem. You can choose to make the swap at the shut-off valves or at the fixture which ever is most convenient. If the lines are the solid copper type you can bend them around to do the job if they are not to short. If line length is a problem I recommend replacing one or both with the flexible type from Home depot or wherever. The type that looks like braided stainless steel is best. Rubber hoses will end up making your water taste funny.

Water heaters draw water into the bottom, and as the hot water heats, it rises and hot water exits from the top.
You might want to check each fixture, does the hot pipe (tubing)feel warm when you run it for a moment. Can you get warm water from some of the fixtures, but not others?
I'm bet there is a leak at the top of the intake which is filling from the top down, instead of bottom up.

If you have a leaking water heater there is a serious problem.
http://waterheatertimer.org/Water-heater-leaking.html
Page shows how to limp along on a leaking water heater if your water heater needs replacement.

One of three things is causing the water:
1) Loose water connection on top of tank that is dripping down inside tank >> check pipes on top of tank.

2) The vent is clogged or not working correctly causing condensation inside flue pipe.
Condensation water is dripping back down inside tank.
Problem means possible CO poisoning if gas is not venting.
Look at vent pipe to see if joints are corroded.
Use long fireplace match > light match and put into draft hood at top of tank and see if smoke goes up.
Put hand at draft hood opening when water heater turns on to see if vent gas enters home.
Do same test when furnace turns on to see if furnace vent is pushing back into water heater.
Does water heater vent inside same pipe as furnace? You may need to set up separate vent for water heater if furnace gasses are pushing back into home.
Check furnace vent for obstructions.
Look at vent stack top of home to see if hood is in place.
Check if bird nest is built inside warm vent pipe.
Improper flue is top priority for getting fixed so vent gasses properly escape home.
You may have to call a plumber.
Professional plumbing forum:
http://www.thetankatwaterheaterrescue.com/forums/forum3/

3) Your water heater is rusted out.
A rusted tank has to be replaced.
It cannot be repaired.
However, before replacing tank, you do not want a tank failure where tank ruptures and water runs inside home until water is shut off.
This will cause major damage.
Protect yourself first.
Turn off water valve above tank.
Move gas knob to 'pilot' so burner is not heating water.
Open tub spout on hot side to relieve pressure on tank so it will not rupture.

Now you're protected.
Link above shows how to limp along on failed tank until you can replace heater.

You need a new gas water heater from Lowes or Home Depot
Look at label on side of you tank for gallons and btu's of your water heater.
Measure height to flue pipe so you get same height water heater, so pipes don't have to be changed.
You need a pipe wrench and teflon tape which will be wrapped on each pipe thread when pipes are reassembled.

Step1) Drain water heater using valve at bottom of tank.
http://waterheatertimer.org/Water-heater-will-not-drain.html

2) Turn off gas valve going into heater.
When gas valve is perpendicular to gas line, then gas is off.
Dissemble gas line to water heater.

3) Disconnect flue pipe and support flue pipe with wire so it doesn't not fall down. Flue pipe joints should be held together at each joint with 3 screws.

4) Turn off water. Shut off valve is on COLD side.
Disconnect water pipes.

5) Move old water heater out of way.

6) Set new water heater in place. Put water heater in drip pan.

7) Connect water pipes >> cold goes to side marked cold.
Hot to hot.
Buy new flexible water connector pipes at home center for easy installation of water pipes.

8) Connect gas line exactly as it was connected before.
Home center sells flexible gas line connector for easy installation of gas line.
To test for gas leak after installation, mix liquid soap with water and put around gas line joints to see if there are bubbles.
Natural gas has less pressure than water lines, so gas pipes are easy to seal with ordinary wrench.

9) install TP pipe that runs to floor. Use old one off old heater.

10) Fill tank completely with water until water is coming out of tub spout.

11) Turn on gas, and light pilot as shown in manual.
New gas heater sometimes have small water leak when first fired up, so ignore a bit of water.

12) Save water heater manual like it is gold, and read everything in manual.

It sounds like two problems.
Problem 1) Clog inside faucet or clog inside pipes at faucet
Remove supply tubes leading to faucet and see if problem is inside pipes or inside faucet.
My bet is clog inside faucet.

If you have galvanized pipe that meets copper pipe, this can be trouble spot.
Article on clogged water pipes at Inspectapedia:
http://www.inspectapedia.com/water/Water_Pipe_Clog_Repair_Guide.htm

Article on clogged pipes:
http://www.waterheaterrescue.com/pages/WHRpages/English/Troubleshooting/Tanklets/backflushing.html

Problem 2) Water heater leak ... you say tank valve is leaking? Is that cold-water shut-off valve? Or tank drain valve? Or TP valve?

If cold water shut-off is leaking, then replace shut off.

If tank drain valve is leaking, then check if plastic valve is cracked. If drain valve is cracked, then replace with a brass valve from Home Depot. If plastic valve breaks off, then use hammer and screwdriver to gently chip out the broken plastic valve. New valve threads need teflon tape to seal pipe. If valve is just dripping, then put garden-hose cap over end of valve and screw down tight.

If TP valve is leaking, then replace with same temperature and pressure rating. New TP valve threads need teflon tape to seal pipe.

Problem 3) If pressure is low all over house:
Buy pressure gauge at hardware store that screws onto hose connection.

Test pressure on outdoor spigot.
Open faucet and check if pressure drops. This says if problem is inside pipes that enter house.

Test pressure on water heater drain valve.
This says if pressure problem is before -or- after water heater.

If problem is before the water heater, then shut-off valve located on cold water line is suspect.
If problem is after water heater, it could be in hot water outflow pipe on top of water heater, or a nearby elbow.
Remove hot water line leading from water heater and check pressure. This says if problem is where hot water leaves tank.
Read articles above about clogs inside water lines.

Believe it or not one of the sink or shower fixtures is by-passing when closed.Gravity circulation in standby mode(not being used) is the cause.Trace the (warm )cold water pipe to the fixture after no one uses the water for a while.Good luck.

if the line feels cold its the fill line if warm its the hot line either line try to tighten the connection if no good or leak is from solder or connection if u have valves to and out shut them off or turn off main open a faucet relieve pressure at heater either solder the line to repair or if connection Teflon tape joint and retighten connection good luck and thanks for using fixya

A few things you should check:

1. Cross Connections - this occurs when cold water leaks into the hot water system through a fixture. In order to check for a cross connection: 1) turn off the cold water to the tankless 2) open up hot water fixtures in the home. The water should shut off at all hot water fixtures; if there is a continuous flow of cold water, then you have a cross connection. The most common place to find a cross connection is on old shower cartridges.

2. Ask the customer to check to see if the burner indicator is continuously lit during operation.

3. When the water goes cold at one fixture, try another near by fixture to confirm it is also cold there. If its hot at one fixture but not the other, then you have some issue with you plumbing. Tankless heaters can't pick and choose which fixtures to deliver hot water to.

4. Tankless water heaters all have a minimum flow rate that must be maintained in order to continually fire (.5 gpm for Noritz). Ensure their hot water fixtures flow at least this amount, or that the customer isn't mixing too little hot water at their fixture.

5. If they see the cold spurt during initial firing, they may be experiencing a cold water sandwich. When the heater moves from a standing state to a firing state it takes a short period to ignite and heat water. During this time it will be passing cold water through the system. Usually this cold water mixes with hot water in the line as it travels through the plumbing system, but if their fixture is very close to the heater, there won't be enough time to mix.

6. If debris has gotten into the flow sensor, this can prevent the unit from registering flow and cause intermittent firing.

You need a recirculating line. You will have to hire a plumber to run a water line from the farthest fixture or to the fixture you are concerned about on the hot side and return it back to the water heater. this will cause hot water to constantly run throught the hot water line (via the recirculating line) and when you want to draw water from the fixture, you will already have hot water right at the line.
I know this works with standard tank water heaters, but it is a lil trickier with rinnai units(but very possible) if your plumber pleads the 5th and tries to sell you another unit call the Rinnai manufacturerand ask them how.

What is your reason to have a recirc line on your water heater does the heater sit to far away from a certain fixture? If you put a pump on your tankless waterheater then your heater will continually fire till the call for hot water is stopped. Yes you normally do need a seperate line installed for a recirc line usually from the water heater to the farthest fixture away. If your problem is taking to long to get hot water then I suggest installing a second heater closer to problem area.