Welcome to the forum. The owner deductions are for charges such as post production transmission, marketing, etc. The check stub should have a run statement that lists what the charges are. It goes back to what was allowed on the original lease. They are very common.
If you are receiving a royalty check, then you are a mineral owner according to the records of Antero. You need to ask them for a copy of the paragraph of the title opinion that lists your chain of title. You need to keep that for your heirs. Keep your check stubs for at least seven years as you will need them for income tax purposes. The check will have the Antero address on it. You need to have a will or trust that passes the mineral rights to your daughters. They will have to settle the estate and give the operator their new addresses and file the estate papers in Tyler County. The surface owner may or may not also be a mineral owner. Keep all your records. You can go to the Tyler County Courthouse and see if they will help you find the original lease.