Is expiation required for one who swore falsely to her father to avoid his anger at her sister, knowing that Sheikh Abdul Rahman Khalif fatwa was that it is an Al-Ghamus oath for which there is no expiation other than seeking forgiveness?

The oath mentioned is a Ghamus oath (a false oath taken knowingly), which is one of the gravest major sins. It immerses its taker in sin, and repentance and seeking forgiveness for it are obligatory. Fear of the father's anger is not considered a justification for swearing a false oath, as it was possible to use allusions (Ma'aridh). Obedience to Allah takes precedence over the parents' رضا (pleasure). There is no expiation for it according to the majority of scholars.