The custom of Sephardim is not to put on Tefillin during Chol HaMoed. The custom of the Ashkenazim in Eretz Yisrael is not to put on Tefillin. In Chutz Laaretz many Ashkenazim put on Tefillin. Therefore, if you have no custom from your father you should not put Tefillin on during Chol HaMoed.
Explanation:
Gemara Menachot 36b: R’ Akiva said we might think that you put Tefillin on Shabbat or Yom Tov the passuk says, “V’haya L’Ot…” only those who need a sign need to wear Tefillin, Shabbat Yom Tov are themselves an Ot.
The Gemara in Shabbat 62a: Abbaye asked on e who finds Tefillin (on the road on Shabbat) should wear into the city pair by pair (wearing them), man or woman. If you say women are considered a nation by themselves it is Shulchan Aruch it is a timebound mitzvah and women are they are exempt. He is of the opinion that one must wear Tefillin at night and also on Shabbat so it is timebound.
The Shulchan Aruch (OH 31:1) On Shabbat and on Yom Tov is forbidden to wear Tefillin since they are themselves are an Ot and if we put on another Ot (Tefillin) it is degrading to them.
The Rishonim discuss what is the Ot of Shabbat?
Rashi in Menachot 15b DH Shehein: it is an Ot between Hashem and Bnei Yisroel as the passuk says, “Ot he…”
The Ritva in Eiruvin writes Since it says the prohibition of doing Melacha on Shabbat is the To.
The Rama Mipano (Shut 108) argues that the Ot is not because of the prohibition to do Melacha, rather it is holiness of these days themselves which are considered an Ot that would not have been revealed unless Hashem commanded Moshe Rabbeinu to reveal them.
The Tosfot in Menachot (36b Dh Yatzu) writes it is not because of the prohibition doing Melacha that it is called an Ot because we see on Chol HaMoed which we are permitted to do Melacha, it is also called an Ot since on Pesach we are forbidden to eat Chametz and on Sukkot we’re obligated in siting in a Sukkah.
There is a Machloket between Rashi and Tosfot is the Ot the prohibition of Melacha and therefore on Chol HaMoed there would be an obligation to wear Tefillin since as Tosfot says there is not prohibition. According to Tosfot the Ot is Pesach and Sukkot respectively then there’s no obligation to wear Tefillin on Chol HaMoed.
Those opinions like Rashi bring two other sources for the obligation to wear Tefillin on Chol HaMoed.
In Gemara Moed Katan 19a there is a machloket between R’ Meir, R’ Yehuda and R’ Yossi whether one is allowed to write Tefillin on Chol HaMoed, not for parnassa or hefsed. On Chol HaMoed we are only permitted to write if it is needed on Ch HaMoed. It must be we are obligated to wear Tefillin on Chol HaMoed
Tosfot discounts this proof since it is possible R’ Yehuda dn R’ Meri are of the opinion that we wear Tefillin on shabbat and it is an Ot also.
The second proof is from a Yerushalmi (Moed Kattan3:4) clearly states that Chol HaMoed is the time for Tefillin. The Gra (OH 31:4) says that the sugya is according to the opinion that one wears Tefillin on Shabbat. He concludes that there is no opinion that one should wear Tefillin on Chol HaMoed.
The Or Zarua says the machloket about wearing Tefillin on Chol HaMoed is dependent on whether doing Melacha on Chol HaMoed (where it is not to stave off financial loss), is from the Torah or Rabbinic. If the prohibition to do Melacha on Chol HaMoed is from the Torah then Chol HaMoed is just like Shabbat and therefore we should not wear Tefillin. But if it is Rabbinic then Chol HaMoed would be obligated in Tefillin.
The Turei Even adds that the Yerushalmi which says you should wear Tefillin is only because the Yerushalmi understands Melachah on Chol HaMoed is Rabbinic.
The Shulchan Aruch (OH 31:2) decides: ON Chol HaMoed it is forbidden to put on tefillin since the days of Chol HaMoed are also a sign. The Rema says there are those who say we are obligated Tefillin and that is the custom of of Ashkenazim just we should not say the bracha out loud since it is a doubt.
The Minhag for Ashkenazim in Eretz Yisroel is not to put on Tefillin.
The Mishna Berura writes if someone has an existing custom to put on tefillin fine, other wise one shouldn’t not change it.
