Āvasathya agni is mentioned in Mahābhārata , while describing different types of Agni.

Āvasathya agni is the fire contained in a small oven that used be required in Vedic yajña. This triangular oven would be of 25 fingers in length, and fire was brought to this oven from Gārhapatya agni. Āvasathya agni was placed towards the east side of Sabhyāgni. The term Āvasatha denotes the place of habitation, as it is proved from the mantra of Atharvaveda —
yad āvasathān kalpayanti.

But from Āpastamva Śrautasūtra , it appears that āvasatha is the place of the guests̍ lodging. Possibly this āvasathya agni was kept burning in this guest house. The reason for this conception is perhaps that by sabhā, it meant, in those days, a court or assembly for the playing dice, and there sabhyaāgni was kept burning– agreṇāhavanīyaṃ sabhāyaṃ sabhyaḥ, according to Āpastamva Śrautasūtra. In the annotation of this sūtra, Rudradatta has written, ̍sabhā dyūtaśālā. tatra sabhyo̍gnirādheyam. Then comes the next sūtra– taṃ pūrveṇa āvasatha āvasathyaḥ– here, the annotator writes– āvasathaḥ atithīnām vāsabhūmiḥ.

So, āvasatha is the resting abode of the guests and in the guest-house, āvasathya agni is to be kept burning.

We can understand, āvasathya agni was placed beside sabhya agni, and perhaps for this reason, in Vāyupurāṇa,. both sabhya agni and āvasathya agni are referred to as the two sons of āhavaniya agni. Actually sabhyagni was placed in the court of dicing, and the guest house for the players, who used to come from distant places, was located towards the east of this court, and in that guest house, āvasathya agni was placed. In this very Śrautasūtra it is said that, āvasathya agni could be kindled from any ordinary fire, or it could be drawn from āhavanīya or gārhapatya agni.

In Vāyupurāṇa it is said that āvasathya agni is the son of ̍śaṃsya̍ agni, and brother of sabhhya agni. This śaṃsya agni is basically āhavanīya agni. For kindling āvasathya agni, fire was drawn from āhavanīya agni — perhaps that is why this father-son concentualisation.
tathā sabhyāvasathyau vai śaṃsyasyāgneḥ sutāvubhau.

This correct version of Vāyupurāṇa mistakenly reads as ̍sava̍ and ̍apasavya̍ in Brahmāṇḍapurāṇa.