。
She stared at me suspiciously.
Literal
She [topic-は] suspicious-looking [adverbially-に] me [object-を] intently looked-at.
じっと is a 擬態語 — a state mimetic — for fixed, motionless attention; it pairs with verbs of watching, listening, holding still, enduring. The evidential frame ~そうに (an i-adjective minus い + そう + に) again turns 疑わしい ('suspicious') into a manner adverb describing how the look appeared from outside. Compared to the smoother 見つめる ('gaze at'), じっと見る adds the sense of an unwavering, fixed stare — the eyes locked on, unwilling to slide away.