Is saying "Yarhamuk Allah" (May Allah have mercy on you) to someone who says "Alhamdulillah" (Praise be to Allah) without sneezing considered mockery, and is it sufficient to repudiate the doer?

It is not permissible to rush to accuse people of mockery without clear proof, especially if the matter is not clear to you, and it appears that you have intrusive thoughts (waswasah) regarding this issue. We advise you to turn away from this and to assume the best of Muslims, in accordance with the Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." Ibn Kathir interpreted the forbidden assumption as accusation and suspicion in an inappropriate context. He mentioned the saying of Umar, may Allah be pleased with him: "Do not think ill of a word that comes from your brother when you can find a good interpretation for it." Ibn Majah narrated from Ibn Umar, may Allah be pleased with them both, that the Prophet, peace and blessings be upon him, said: "The sanctity of the believer is greater in the sight of Allah than your sanctity [referring to the Kaaba], his wealth, his blood, and that one should not assume anything but good of him."