Is it permissible for a Muslim to ask God to grant him supernatural power?

The failure to specify the nature of the request in the question makes the answer general. However, asking Allah for what is usually impossible, such as requesting to fly or to attain the ranks of prophets, is considered an transgression in supplication. Allah does not love transgressors, as He Almighty said: "Call upon your Lord humbly and privately; indeed, He does not like transgressors."