様(よう)な気(き)がするHave a feeling that

ような気がする and そう both express impressions, but with different nuance. ような気がする conveys personal intuition or vague feeling, i.e. something you sense even without clear reason. On the other hand, そう is typically based on observable clues or appearance. In that sense, ような気がする is more subjective and less confident than そう.

ように・ような follows the plain form of a verb or adjective, and expresses similarity in a general sense. For example, 春が来たような日 'a day that is like as if spring had come'. ような気がする is a common idiom that uses this pattern, meaning 'have a feeling.' For example, 誰かが来たような気がする ('I have a feeling that someone came.').

Both ような気がする and ぎみ (from 気味) use 気 expressions to convey subtle states or impressions, but with different nuance and usage. ような気がする follows a phrase to express a subjective hunch like 'Have a feeling that (A)', e.g. 来るような気がする 'I have a feeling they'll come.' ぎみ attaches to nouns to express a slight tendency or hint of something observable, often (but not always) negative, e.g. 疲れ気味だ 'I'm feeling a bit tired.'