What is the ruling on someone who entered into the state of ihram for Umrah from Abyar Ali without stipulating any condition, then was prevented from entering Makkah? Is there an expiation upon him, and what is its amount, and must it be distributed within the Haram?

What happened was an ihsar (being prevented from completing the pilgrimage). If you performed tahallul (exited the state of ihram (definition)) by shaving or shortening your hair with the intention of tahallul along with offering a hady (sacrificial animal), then there is no problem. However, if you returned to your place of residence and did not perform tahallul, or you performed tahallul without a hady despite being able to offer one, then you and any of your children who are adults are still in a state of ihram. If you have not yet performed tahallul, then do so by slaughtering a hady for each individual, the minimum of which is a sheep, to be distributed among the poor in that land. If you are unable to do that, then for each adult individual, fast for ten days instead of the hady, and one should not perform tahallul until after completing the fasting. As for young children, they are not obligated to complete the rituals, nor are they required to offer a hady.