Is "Indeed, a servant is deprived of provision by a sin he commits" an authentic Hadith, and how do we reconcile it with Allah's saying: "But Allah would not punish them while you, [O Muhammad], are among them, and Allah would not punish them while they seek forgiveness," and does seeking forgiveness after committing a sin prevent the deprivation of provision?

Being deprived of provision due to sin has two meanings: it could refer to the reward in the Hereafter, or to worldly provision such as wealth, health, and well-being. This is specific to the Muslim, so that Allah may elevate their rank in the Hereafter. As for Allah Almighty's saying: "And Allah would not punish them while you, [O Muhammad], are among them, and Allah would not punish them while they seek forgiveness," the meaning is that Allah would not punish them due to the presence of the Prophet (peace be upon him) among them, and due to the Muslims seeking forgiveness. Seeking forgiveness brings good and wards off evil, while sin and turning away from Allah lead to deprivation and hardship. There is no contradiction between the verse and the hadith (definition).