I've come across this sentence with ~まいて after a verb. I've never seen it like that before, but I'm assuming it is a form of ~済まい:

「いくらも進んでおりませぬよ。儂の命のあるうちに終わりますまいて」

I can't make any progress. It probably won't end during my lifetime.

If it is ~済まい, what does the て do here...?

I've come across this sentence with ~すまいて after a verb. I've never seen it like that before, but I'm assuming it is a form of ~済まい:

「いくらも進んでおりませぬよ。儂の命のあるうちに終わりますまいて」

I can't make any progress. It probably won't end during my lifetime.

If it is ~済まい, what does the て do here...?