Hi,
I bought a condo ( as a second residence in another state) paying cash which I borrowed as a line of credit on my primary residence. I put my son's name also on the deed, so that he can take care of paying the dues, taxes etc. when needed, because he lives there. He moved into the condo for free and did not pay any rent.
We applied for another line of credit on this condo , on my son's name so that he can use that money as a down payment for him to buy a property on his own. Over 2 years period I paid off the loan ( on my own) that I borrowed on my house and he did not buy any property. So the line of credit on the condo was not used for 2 years. Last year he borrowed $ 70,000 ( with my permission) on that and paid as a down payment to buy a new house for $370,000. This helped him to qualify for his mortgage and he gave the condo for rent.
We both have got into some conflicts due to his actions. This year I came to know that he borrowed $100,000 instead of $70,000 and he is not paying regularly the payment for the line of credit , in spite of taking the rent from the condo. Now I want him to quit claim on this condo.
Could he deny to sign the quit claim deed? If he denies what are my rights to remove his name legally? I paid the whole money and I have the transaction papers to prove it.

Yes he can deny to sign, you can't force him to sign over his share of the deed. ( that is why when you put someone on a deed, you have to be sure, since depending on how they are on it, joint in common or with 1/2 ownership.

Also since his name is on it, if he goes broke, they can put a lien on his share for money he owes others.

Your only recourse is to sue your son to return the extra money he took and the proceeds of the rental.