You can deduct real estate taxes paid in 2016 on your 2016 tax return (the June and September payments). You can also deduct real estate taxes paid at closing if you are the seller.
For the home you purchased, you can deduct real estate taxes that you paid at closing if those taxes were actually sent to the taxing authority. If the amount paid was placed in escrow with your mortgage holder, you cannot deduct them until the year they are sent to the taxing authority.
See
https://www.irs.gov/publications/p530/ar02.html for more information.