Installed timing belt and put everyting back but know my toyota runs rough, Have cheaked many times if timing was wrong. but its is, what can it be ???

With a loose tensioner...There are timing marks on the crank. Line it up, run your belt up and around cam pulley which will also have timing marks. If it is duel cam marks will line up with each other. Keep all the slack of the belt pulled to the side of the tensioner. Release the tensioner and confirm marks. Turn motor through a revolution by hand and reconfirm marks are lined back up. Put it all back together.

1. Error Code 24. Intake Air Temperature Sensor.
Solution:
Check the following:
- IAT Connector and wiring.
- Intake Air Temperature Sensor.
- Engine Coolant Temperature Sensor.
- ECM.
2. Rough Idling when the engine is hot.
The following are the reasons due to which the engine can perform bad when it is hot.
- Fuel pump control circuit.
- Fuel pump pressure.
- Fuel injectors.
- Non Return Valve clogged, located on the lower side of car chassis above the fuel tank.
- Engine compression, valve clearance, spark plugs.

The previous owner has screwed things up by changing the air intake and eliminating the air temp sensor. The car's computer depends on a series of sensors to determine what fuel mixture it should command, and now it can't do that properly.

When the car is cold, it knows from the coolant temp, and it sends plenty of fuel, but when hot it is getting the mixture wrong.

Restore the air intake to original, with the correct sensors, as it should run OK.

If not, then go looking for a vacuum leak or an air leak in the air intake hose and plenum somewhere.

if belt was not put on properly car wont run. if its improperly timed valves are opening and closing when they shouldnt be. which inturn will not ,ix air gas and timing spark. when belt is on wrong it will seem like no compression because valves are improperly working. belt must be put on the rite way for your car to run.

suspect the timing belt tension was to low and has jumped a few teeth initially(run rough) and then jumped further or stripped teeth(will not start at all).
check timing belt position setup....
if its 1-2 teeth out of timing you could put a new belt on with engine correctly setup.
.if its completely wrong the your engine will have internal damage(valves bent and pistons dented)

Take it back to your mechanic RIGHT AWAY. Provided of course it didn't do this before my best guess is the timing belt is off several notches and continued starting of this car could cause a lot a damage.Have them come and pick the car up, there is something major wrong here! Good luck

You are right--they did something wrong, either the wrong belt or incorrect belt routing. Most likely they used a too-long belt. Take it back and complain.

You most likely threw the timing off when you changed the timing belt.. Even throwing the timing off 1 tooth can cause it to run very rough.. I would check the timing marks on the belt and make sure they align with the marks on the timing gears. Good luck

firstly you have to reduce idle srew,and cheak for any damage vaccum,cheak the feul filter for dirty for rough runing

i would first check the timing and if that does not fit i would take the cover back off and look at the belt for a bad or missing tooth