Is a man permitted to have the kippah that he is wearing resting on the straps of the shel rosh tefillin that are on his head? Perhaps it would be forbidden because it would be a secular object resting on a holy object.
Rav Dovid Feinstein can be seen wearing his yarmulka on in his tefillin straps:
In Sefer Daas Noteh, Rav Chaim Kanievsky, in footnote 15, notes that it may not be correct to have one's hat resting on one's actual tefillin shel rosh, but writes that it's not actually forbidden from din since its needed for tefillah. So the yarmulka is necessary for teffilah and it's not on the same level as the teffilin themselves ,so certainly it cannot be forbidden according to halacha.