My car suddenly started showing the check sign and then bring out black smoke from the exhaust. It also hesitates in acceleration

Is the smoke white or black? If it's white head gasket black it oil .

Black smoke is usually a sign of too much fuel.
Check the injectors and the air filter for problems.

Probably not a problem as black smoke is a sign that too much fuel went into the engine. This is especially true when engine is cold and in choke or "cold start sequence".

White smoke coming out of exhaust is water vapor. Blue is oil burning and black is carbon from unburned fuel.
U have water or coolant leaking into your combustion cylinders - not a good thing. Probably blown head gasket.

Check your oil - if it like a brown mud then the coolant has also gotten into the lubrication system.

bad water pump maybe

overheating? low oil in crank case?low coolant ,maybe have catalytic converter checked if smells like rotten eggs!!!

Sounds like either the float level is too high, there is a problem with the float needle valve or the power valve is stuck. I'd take the carb off and either replace it or take it apart and check everything inside. If you do nothing, chances are it will either get worse or if it's a small piece of junk inside, it may clear up by itself...I'd take it apart. Since it's pretty new, if you are careful, likely you won't need a gasket kit.

When did you last replace the air filter?
Check the air filter it may have been clogged by dust.
If its (air-filter) ok thn you will have to get the injector pump and the injector nozzles serviced.
Hope this helps!

Black smoke from exhaust means engine getting to much gas.

Black smoke from exhaust means engine is getting to much fuel