What is the Sharia ruling for a wife who suffers from her husband's abuse and confinement, and is it permissible for her to not fulfill her marital obligations towards him if she fears Allah?

If what the questioner mentioned is true, then it is not permissible for the husband to do that. He must either keep his wife honorably or release her kindly. The wife has the right to seek a divorce when there is harm and abuse. Such matters are referred to the Sharia court, because resolving them requires evidence and witnesses, as the Prophet (peace be upon him) said: "But the burden of proof is on the claimant, and the oath is on the one who denies." The judge's ruling does not make lawful what is unlawful nor make unlawful what is lawful between the servant and Allah Almighty.