We read in Parshat Pekudei 40:27-28:

וַֽיַּעֲשׂ֛וּ אֶת־הַכָּתְנֹ֥ת שֵׁ֖שׁ מַעֲשֵׂ֣ה אֹרֵ֑ג לְאַהֲרֹ֖ן וּלְבָנָֽיו׃ וְאֵת֙ הַמִּצְנֶ֣פֶת שֵׁ֔שׁ וְאֶת־פַּאֲרֵ֥י הַמִּגְבָּעֹ֖ת שֵׁ֑שׁ וְאֶת־מִכְנְסֵ֥י הַבָּ֖ד שֵׁ֥שׁ

They made the six tunics of woven work, for Aharon and his sons; and the six headdresses, and the six decorated turbans, and the six pairs of linen breeches.

By my count, they only needed five sets of bigdei kehuna - for Aharon and his four sons: Nadav, Avihu, Elazar and Itamar.

For whom was the sixth set of bigdei kehuna made?

This question is Purim Torah and is not intended to be taken completely seriously. See the Purim Torah policy.

The verse that you quoted says that these six sets were "for Aaron and his sons". In fact Moses needed a set, for, as we know, he served as priest for the week that the tabernacle was being inaugurated. That's the sixth set. Why does it call him Aaron's son? As Rashi (Numbers 3:1) explains:

שכל המלמד את בן חברו תורה מעלה עליו הכתוב כאילו ילדו

whoever teaches his friend's son Torah, it's as if he fathered him.

Since Moses taught Aaron's son Torah, it's as if Aaron fathered Moses.

one for aharon during the year and one for yom kippur

better question is what is a mitznefes-headdress? is that a dress for the head or a sheitel head to keep dresses on?