He transferred money from his account to his cousin’s account so he could go to the bank and withdraw it, in return for a fee

There is nothing wrong with transferring money from your account to your cousin’s account, so that he could withdraw it from the bank and give it to you, in return for a fee for doing this procedure.

The money that went into his account was your money, which he was going to withdraw from the bank, which is a permissible action for which it is permissible to receive a fee. But if he gave you the money before it was transferred to him, then this is a loan from him to you, and it is not permissible for him to take anything in addition to that, because that is riba (usury).

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (6/436): Every loan in which it is stipulated that something extra be given is haraam, with no difference of scholarly opinion concerning that. Ibn al-Mundhir said: They [the scholars] were unanimously agreed that if the lender stipulates that the borrower should pay back something extra or give him a gift, and he gives the loan on that basis, then taking something extra in return for that is riba. It was narrated from Ubayy ibn Ka‘b, Ibn ‘Abbaas and Ibn Mas‘ood that they forbade loans that bring benefits. End quote.

If he was going to give it to you before it was transferred to him, then he should have done that for free.

And Allah knows best.