Is the supplication, "O Allah, subject to me the angels of the heavens and the earth," correct? And is there any error in it, considering that angels are not subjected to an ordinary human?

Angels are not subservient to any person, but Allah may assign some of His angels to aid or assist certain individuals, as happened at Badr and with the guardian angels who protect humans, based on His (the Most High) saying: "For him are successive [angels] before him and behind him who protect him by the command of Allah." This also occurs for some regular mosque-goers, as in the hadith: "Indeed, for mosques there are pegs (regular attendants) who are their pegs. They have companions from the angels. If they are absent, [the angels] inquire about them. If they are ill, they visit them. And if they are in need, they assist them."