The two main deductions you normally would have are for property taxes and mortgage interest. It sounds like you don't have a mortgage, so the latter would not apply to you.
I believe you can only deduct property taxes paid for the period of time applicable to when you own the home. Property taxes are usually paid in advance, either once or twice per year for the following six months. So in principle you should be able to deduct all of the property taxes you paid this month plus a prorated portion of what your Dad probably paid last December. Normally these amounts would be calculated for you and listed on your closing or settlement statement, but since you did a quit claim you probably didn't have a traditional closing and may have to prorate those amounts yourself.
The last thing I would be worried about in terms of taxes is that the quit claim from your father to you might constitute a gift and be subject to gift tax. The short version here is that the first $14,000 or so of gifts from any one person to any other person are free of gift tax, but beyond that amount are subject to gift tax. Your father could choose to use up part of his lifetime combined exclusion to cover this - he would have to file a form with his taxes for this year, and you would need to account for that gift when calculating his estate tax return when he passes away.