The term ‘savya‘ means the left side. Apasavya is side which is not the left, that is, the right side. In Rāmāyaṇa (Ramayana), apasavya has been used in this sense, while describing Prahasta’s venture to battle. While Prahasta was going to fight, the Rākṣasa(s) (Rakshasa; one kind of demons) were loudly shouting, and the vultures, feeding on flesh and blood were moving on the right side of his chariot —
maṇḍalānyapasavyāni khagāścakrū rathaṃ prati.
In Mahābhārata (Mahabharata), apasavya has been used in the sense of contrary or antagonistic — “If my words seem antagonistic to you” —
yadyetad apasavyam te bhaviṣyati vaco mama.
Nīlakaṇṭha (Nilakantha), the commentator has explained its meaning as —apasavyaṃ viparītaṃ yadi.
In technical usage, while performing the śrāddha (sraddha; rites dedicated to the deceased spirit), sometimes the sacred thread has to be shifted from the left shoulder and put on the right shoulder and that should be passed under the left arm, the process is called apasavya.