Is there a fee required for submissions under 37 CFR 1.501?

No, there is no fee required for submissions under 37 CFR 1.501. According to MPEP 2205:

No fee is required for the submission under 37 CFR 1.501.

This means that anyone wishing to submit prior art or patent owner written statements under this rule can do so without incurring any official fees. This policy encourages the submission of relevant information that may be pertinent to the patentability of the claims in a patent.

To learn more:

Topics: MPEP 2200 - Citation Of Prior Art And Ex Parte Reexamination Of Patents, MPEP 2205 - Content Of Prior Art Or Section 301 Written Statements, Patent Law, Patent Procedure
Tags: 37 Cfr 1.501, Prior Art Submission, Submission Fees