Is there any way I can request a transcript tax return if I was one of the dependents ?

No.  The taxpayer whose name is on the tax return can request a transcript.  You cannot get a transcript of a return that you were claimed on as a dependent.  What are you trying to do?  

Im going through the process of verification for my university and the are asking me about my 2018 tax return. But my cousin claims to have never received the taxes it got rejected when I asked if he can give me the transcript for nun financial aid. I don’t know if he is hiding something. And sadly I won’t get awarded financially at my university with out the tax return.