It depends on the sentence. Paramin olduğunu is not wrong, it could mean "that is of my money" while param olduğunu could mean "that is my money". Ofcourse in a sentence it would translate differently. I found this sentence:

Ne kadar kalacağımı, neden geldiğimi, ne kadar yanımda paramın olduğunu, gideceğim adresi sordu.

He asked how long I will stay, why I came, how much (of my) money I have with me, and the adress of where I´m going.

which ist correct ?

Parasi olmadigini soyledi.

or Parasinin olmadigini soyledi.

please ignore the wrong spelling

and how ist translated in turkish

. I told them that I have a girlfriend.

and : He told me that he had a sister.