What is the ruling on one who swears an oath without completing the word of majesty (Allah), such that they do not pronounce the letter "hā" (هـ), knowing that it is their habit to pronounce the "hā" when swearing, and what is the opinion of the majority on this issue, and what is the most preponderant view?

This issue is a matter of scholarly disagreement:

Some scholars are of the view that omitting the letter Hā’ (هـ) from the word Allah (الله) in an oath prevents the oath from being binding. Others are of the view that it is binding, as a concession. Still others are of the view that it is binding if there was an intention to make an oath, and this last view is the most plausible. Ibn Abidin mentioned the اختلاف (disagreement) among jurists regarding the validity of an oath when the letter Hā’ (هـ) is omitted or the Lām (ل) is extended, and he urged against leaving it out as a precautionary measure. Al-Shabramallisi mentioned that the most plausible view is that the oath is not binding when the Hā’ (هـ) is omitted, because it is not one of Allah’s names without it. However, it is possible for it to be binding if there was an intention to make an oath and the omission is interpreted as a concession.