The forms you signed at closing will specify how property tax was handled. At closing, depending on the due date of the next tax bill, and the period it covers, either you gave the seller money to pay part of the bill or they gave you money for part of the bill.
A part of each monthly payment is allocated by the lender to set aside for property tax. Depending on the jurisdiction there could have been one of two instances in each year where property taxes are paid by the lender from the escrow account for property tax.
You will be able to claim what was paid by the lender for the property taxes, then adjust it by what is noted in the settlement documents.
You can and should go to the local jurisdiction's website to see the property taxes for your property. You do want the bill sent to the lender, and they want the bill sent to the lender. But you want to review the record to make sure that the bill makes sense.
Keep copies of the tax bill, the 1098 from the lender, and the document from closing.
when you own the property for an entire property tax year, the amount that the lender sends to the county should equal the amount on the tax bills, and will be the amount that you include on your taxes. In the first and last year you own the property that won't be true because you don't own the property for the entire year, and the adjustments on the settlement documents.
The amount that lender sends to the local government may or may not equal the amount that they have been setting aside for property taxes. This is because many local jurisdictions adjust the value each year and the property tax rate each year, which means that sometimes too much or too little is withheld. The lender will generally notify you if they have to adjust the escrow amount.