We have a 20 year old Bryant electiic furnace and the blower and the heat will not shut off unless you trip the three brackers on the furnace. The fan relay has been replaced and a new thermistate installed but did't fix it. The thermastate has no effect . With it turner off the heat anr fan still run.

It could be the heat sequencer. On many Bryant units the heat sequencer also activates the blower in the heat mode. They look somewhat like this. If you tap on it with a insulated tool it might stop blowing to confirm it is defective if not you will need to test with a meter or just replace. There should be a part number on the heat sequencer.

This image is just to show what one might look like. There are a few different types.