I am a bit skeptical. Can you share a story from the teachings about how Sai Baba dealt with a doubter?

Certainly. Chapter 35 recounts the story of Boss Dharamsee, who visited Shirdi with a skeptical, 'clinical scrutiny'. When offered grapes with seeds by Baba, Dharamsee was inwardly displeased, as he disliked that variety and worried they were unwashed. He even doubted Baba's sainthood, thinking, 'If he is a saint, how does he not know that I do not like these grapes?' In response, Baba gave him even more. Finally, when commanded to eat them, Dharamsee discovered they were miraculously seedless. This experience shattered his skepticism, causing his ego to drop away and a profound love for Sai to be born in his heart, demonstrating how Baba works with each individual's mindset.