Are there any trustworthy Mathematics fee-based open access journals?
I'll try to link to pages which describe the open-access policy of the respective journals.

Both Proceedings of the AMS and Transactions of the AMS allow the author to pay a fee to make their article freely available electronically from the journal.  If the author chooses not to pay the fee then the article is not freely available from the journal (but the author may post the final preprint on the arXiv or their personal website).

The (few) Elsevier journals I have looked at have a similar fee for publishing open-access.  One example of which is the Journal of Mathematical Analysis and Applications.  You might try their Journal Finder, which has a checkbox to only search for journals with open-access options.

Springer offers a similar program for some of its subscription-based journals which they call Open Choice.  Not all of its journals have this option (e.g. Acta Mathematica doesn't).

We also note that Elsevier and Springer both publish a number of purely open-access journals, but I can't comment on their "trustworthiness".