As a seller you can deduct property taxes for the time you owned the property up to but not including the date of sale even if the taxes were noted as an unpaid adjustment on the closing statement. As a buyer, you are entitled to deduct the property taxes paid that attributable from the date of closing forward.
For illustration purposes, I will use a sale date of 7/1 so that were dealing with an even six months of ownership for both the sell and the buy.
For the sale - if 10 months of property tax was $1401.10 that is $140.11/mth x 6 months ownership (Jan-Jun) = $840.66 deductible on your return
For the buy - if 10 months of property tax was $3477.70 that is $347.77/mth x 6 months ownership (Jul-Dec) = $2086.62 deductible on your return. The amount on your 1098 likely includes as part of the paid amount, the property tax due from before you bought the house and so that part wouldn't be deductible.
The adjustment items are for where the buyer (in both your sale & purchase) gets credit for property taxes that are really the seller's responsibility but that the buyer will pay at a later date.
IRS Pub 530 has a good
example about buying a house mid-year and how to handle the calculation of
deductible property tax amount. It is clear that you cannot deduct property
taxes for a time when you didn't own the house.
