Did Moses (peace be upon him) swear by other than Allah or by the blessing in His saying, the Most High: "He said, 'My Lord, for the favor which You have bestowed upon me, I will never be an aid to the criminals'"? And what is the evidence for the permissibility of swearing by a blessing?

An oath or swearing is not permissible except by Allah Almighty. Swearing by other than Allah, including swearing by a blessing (ni'mah), is forbidden and does not constitute a valid oath, according to the Prophet, peace and blessings be upon him, who said: "Whoever swears by other than Allah has disbelieved or committed shirk (definition) (polytheism)."

As for the statement of Musa (Moses), peace be upon him: "(He) said, 'My Lord, for Your favor (ni'mah) upon me, I will never be an assistant to the criminals,'" the particle "ba'" in (bi-ma) could possibly be causal, meaning: "Because of Allah's favor upon him, he will be thankful."

It is also possible that it is for an oath, and it is well-known that the answer is ellipted, with an estimated meaning of "I will repent" or "I will abstain." According to this interpretation, it is an oath by the Creator's action and attribute (the bestowal of favor/ni'mah), and not by a created blessing. Swearing by the attributes of Allah is legitimate.

The phrase "I will never be an assistant to the criminals" might be understood as a statement conveying a supplication (i.e., "So do not make me an assistant to the criminals"), or as a statement conveying a commitment and covenant (i.e., "I will no longer assist an oppressor in his transgression").