Ṛṣi Yājñavalkya is very venerable & renowned Ṛṣi, not only in itihāsa-purāṇas, but also in śruti.
And in smṛtis, he is a śiromani, being the author of Yājñavalkya dharmaśāstra.
As for the gotra & pravara of Ṛṣi Yājñavalkya, there are two conflicting accounts.
As per Anuśāsana Parva (4.48-60), Yājñavalkya's gotra was Viśvāmitra. And he is called vikhyātaḥ (Ibid., 4.51) & a brahmavādinaḥ (Ibid., 4.60). But Nīlakaṇṭha's commentary Bhāratabhāvadīpa doesn't throw any light on the ślokas mentioning Yājñavalkya to be a Vaiśvāmitra here. Aligning with Anuśāsana Parva (4.45-60), both Vāyu Purāṇa (91.97-102) & Brahmāṇḍa Purāṇa (2.66.66-74) also state that Yājñavalkya's gotra was Viśvāmitra.
The Viśvāmitra gotra-pravara lists in sūtras of Baudhāyana, Āpastamba, Kātyāyana & Laugākṣi, & Matsya Purāṇa (198.2-6), in Puruṣottama Paṇḍita's Gotrapravaramañjarī, state that the gotra of Yājñavalkya is Viśvāmitra & his pravara is tryārṣeya (i.e. 3-ṛṣi pravara such as 'Vaiśvāmitra, Daivarāta, Audala'), and those belonging to this pravara are also known as Kauśikas.
The Vasiṣṭha gotra-pravara lists of Matsya Purāṇa (adhyāya 200) & sūtras of Kātyāyana & Laugākṣi, in Gotrapravaramañjarī, state differently that Yājñavalkya's gotra was Vasiṣṭha and his pravara was ekārṣeya (i.e. one-ṛṣi pravara - Vāsiṣṭha). Since, there are two conflicting positions on the gotra & pravara of Yājñavalkya, there are three possible resolutions -
(i) one of the two accounts is erroneous.
(ii) there might be 2 Yājñavalkyas, one being a Vāsiṣṭha & another a Vaiśvāmitra.
(iii) Vaiśvāmitra and Vāsiṣṭha Yājñavalkya are similar figures from different kalpas, and the difference in gotra & pravara evident in śāstras, might be due to kalpabheda.
The number of sources saying that Yājñavalkya was a Vaiśvāmitra are more than those stating him as being a Vāsiṣṭha. Therefore, most likely the famed Ṛṣi Yājñavalkya was a Vaiśvāmitra (belonging to Viśvāmitra gotra & tryārṣeyapravara such as 'Vaiśvāmitra, Daivarāta, Audala').
Yājñavalkya is called the son of Brahmarāta (brahmarātasuto) in Viṣṇu Purāṇa (3.5.2), and the son of Devarāta (devarātasutaḥ) in Bhāgavata Purāṇa (12.6.64). However, the person named Devarāta here, is not the Rājā Devarāta, in the line of Nimi. According to me, either both the names (Devarāta & Brahmarāta) refer to the same person (highly probable) or possibly at least one of the names refer to an ancestor such as grandfather (rather than a father).
It's hard to know for certain, who are Devarāta or Brahmarāta. But since, Yājñavalkya is a Vaiśvāmitra (most likely), then we can point out that the Devarāta mentioned as his father in Bhāgavata Purāṇa (12.6.64), may most likely be Śunaḥśepa (adopted son of Viśvāmitra), who was also known as Devarāta as per Bhāgavata Purāṇa (9.16.30-33), Harivaṁśa (1.27.54-58), etc. This also seems to align perfectly with the Viśvāmitra gotra-pravara lists (referred to before), where Devarāta is one of the three pravara ṛṣis in the pravara of Yājñavalkya.
And so, we have ascertained the identity of Devarāta.
As per Skanda Purāṇa (6.129-131), Yājñavalkya had a son named Kātyāyana, with his wife Kātyāyanī. Note that this Kātyāyana is the author of śrautasūtras, etc. and not the renowned vārttikakāra of the same name.
kātyāyanaṁ sutaṁ prāpya vedasūtrasya kārakam // (6.129.71b)
jyeṣṭhā cānyātha kalyāṇī khyātā kātyāyanīti ca /
yasyā kātyāyanaḥ putro vedārthānāṁ prajalpakaḥ // (6.130.3)
In his commentary Tattvadīpikā on Vālmīki Rāmāyaṇa (3.19.22), Maheśvaratīrtha reports a story from a dialogue of Bhīṣma (said by him to be found in Mahābhārata, but I haven't been able to locate it), as per which, Khara, Dūṣaṇa & Triśira were actually the sons of Yājñavalkya, in their prev. life, named as Candrakānta, Mahāmedha, & Vijaya respectively. But due to a śāpa from Śiva, they were reborn as rākṣasas. The 14 rākṣasas, who followed them, were their śiṣyas, in their prev. life. Their śāpa was to terminate when Viṣṇu, in his Rāmāvatāra, would slay them. The same is also told by commentary Tilaka on Vālmīki Rāmāyaṇa (3.19.22)
Note: The numbering of ślokas from Mahābhārata, follows the Gītā Press version.