in josaac process in category verification as I belong to ST category in Rajasthan but I live in Gujarat and pass 10+2 from Gujarat. so can there be any problem in admission time
No, there will not be any problem during JoSAA counselling. While filling application, just enter the state of domicile as Gujarat. And if it asks for permanent residence address, I hope it will be in Rajasthan then fill it as Rajasthan and otherwise Gujarat in that column also.
Hope it helps.