I am newly married with my cousin. She is my Father's cousin's daughter. So, now my question is- is there any genetic or other problem to get a baby? I heard that, there is a risk like abnormal baby.so, can you please let me know, is there any test available before taking a baby ?
Please let know your advice.

No, if this was a real "cousin" your aunts or uncles daughter.

This is either a 3rd or 4th cousin,

No there is no issue there, new studies even show that a 1st cousin has very few risks.

So you are safe,