When you buy the condo, you will pay certain closing costs that you can deduct on your tax return as itemized deductions (if you itemize); mortgage interest from the day of closing to the end of the month, a property tax adjustment for taxes that the seller paid in advance, and possibly mortgage discount points. The other closing costs are not deductible but increase the cost basis of the condo.
When you give the condo to your son, you will have to file a gift tax return to report the gift (any gift over $14,000). No tax is owed, unless your total lifetimes gifts to other people total more than $5.4 million, but you need to file the gift tax return so the IRS can count the gift against your lifetime maximum.
Once your son is the legal owner, he can deduct property taxes and mortgage interest if he pays those costs, even if the mortgage is in your name (as long as the deed is in his name.)
However, as soon as you file that quit claim deed, you will be in default of your mortgage and the bank can require immediate repayment in full. In some jurisdictions, the quit claim deed would not even be valid unless the mortgage lender approves of the transfer. (Unless you can buy the condo without a mortgage in which case no problem).
