Is it permissible to pray while sitting when carrying a crying baby who is suffering from a high fever?

The scholars have agreed that standing is a pillar of the obligatory prayer, and it is not permissible to sit except for one who is unable to stand, due to the saying of the Prophet, peace and blessings be upon him: "Pray standing; if you are unable, then sitting." What you mentioned is not an excuse that permits praying while sitting, despite being able to stand, in the obligatory prayer. You can pray when your infant sleeps, or entrust someone else with carrying him, or lighten the prayer without compromising its pillars. As for the supererogatory prayer, it is permissible to sit even if one is able to stand, and you will receive half the reward of one who prays standing. It is also permissible to carry an infant during prayer if you are certain of the purity of his clothes.