Ok. This year I am fasting in rajab and shaban as well but I've read a hadeeth that if we have a qaza roza then its not jaayez for us to fast mustahab fasts

So can I do to qaza fast after the month of this mahe ramzan ends. If no then am I eligible for the reward of fasting in rajab and shaban?

You can fast the coming days with the intention of qaza, and Allah SWT, will give you the reward of the month of Sha'aban as well, then continue the rest of qaza after the holy month of Ramadhan.