Generally people don't wear tefillin after musaf on Rosh Chodesh. There is a discussion in the poskim (which mainly seems to be among the mekubalim) if one would wear tefillin on Rosh Chodesh during Mincha or if they would wear tefillin after musaf in a case where there minhag is to wear the whole day. In those such cases I saw those that allow. However what about in a case of a bris milah? (where there is a minhag to wear tefilling based on what the Shach writes in YD Siman 265 and the Magen Avraham in OC Siman 25) What is the minhag in such a cases? Are there different practices? If so what are the sources for them? Also does it make a difference if it's a source according to kabballah or according to a more halachic stand-point (not mixing in kaballah.)
1related judaism.stackexchange.com/q/3438/759 judaism.stackexchange.com/q/10265/759 This seems pretty similar to the latter case of Bris in the afternoon. In both cases you've already removed them but could in theory put them back on.– Double AA ♦Oct 30, 2016 at 14:03
hebrewbooks.org/pdfpager.aspx?req=55555&st=&pgnum=121– Double AA ♦Jun 16, 2021 at 16:09
Kaf HaChaim 25:96 says one should not put back on the Tefilin for a Bris on Rosh Chodesh.