Bike is TTR600 model year 1999.

I can get the engine running by using starter gas. Without gas it is very difficult, or impossible, to start the engine.

When it starts, it runs for short time, then stalls even if I try to keep the throttle open.
I can hear the engine "losing grip of life"; rpm slowly goes down when on idle.

The problems seems to have started after oil change (filter included).
First I may have over filled it with oil. Run it for short time, then drained out the excess oil.

I have checked air box for excess oil (out from the breather pipe). No oil found in the air box.

I'm puzzled by the root cause of the issue. Maybe related to valves?

All help/advices/recommendations are much appreciated.

The issue starting after your oil change is likely just very coincidental. Are you sure you have fuel in the carb bowl? Fuel drains out of it when you open the bowl drain ata good rate? If fuel flows out of the drain very slowly the internal carb inlet filter may be blocked. Is the fuel level in the bowl correct? Check using clear tube method. If you have fuel then likely pilot jet blockage at a good guess.