The authorship of Apastamba Shrauta Sutra and Apastmba Yajna Paribhasha pertaining to procedures in Vedic yajnas; Apastamba grihya sutra laying down procedures for domestic rituals and Apastamba Dharma Sutra on laws of individual and social conduct is attributed to Sage Apastamba.
There is a story in Brahma Puranam about how he got his name. Once a brahmin was about to perform his yearly sraadha. He could not find a suitable brahmin for varanam in pitrusthana.He prayed to his pitrus, visvedevas and Lord Maha Vishnu. Suddenly a brahmin appeared before him. The Sraadha was conducted. At the end, he was asked tripti ( satisfaction). Honest as he was, he denied satisfaction. If the bhokta denies satisfaction then the sraadha is rendered fruitless. The annoyed performer of the sraadha, cursed the brahmin by taking water in his palm and throwing it on him. The brahmin with his tapa shakti made the water to stop midway. Apa - water. Stamba - stopped still. Thereafter he became known as Apastamba.