My mother passed away in Ohio, and I am inheriting a modest amount from her estate. I live in Texas Will I be subject to Ohio or Texas inheritance tax laws?

Check this
Ohio estate tax - Wikipedia, the free encyclopedia

Neither Ohio nor Texas have inheritance taxes, so you as the heir do not need to be concerned. The tax that the article MukatA referced above is about Ohio's estate tax, which is something the executor of your mother's estate should be aware of, but if any estate taxes are owed to Ohio they would be paid directly out your mother's estate BEFORE distributions are made to the heirs. Same thing with regards to the federal estate tax.