Yes. There are some examples. Children of King Rishabhdeva became Brahmana.

S.B. 5:4:13.In addition to these nineteen sons mentioned above, there were eighty-one younger ones, all born of Ṛṣabhadeva and Jayantī. According to the order of their father, they became well-cultured, well-behaved, very pure in their activities and expert in Vedic knowledge and the performance of Vedic rituals. Thus they all became perfectly qualified brāhmaṇas.

Descendants of King Dhrshta became Brahmanas.

S.B. 9:2:17.Manu also had a son known as Dhṛṣṭa, from whom another sect of kṣatriyas was generated, but although they were born of one who had the qualities of a kṣatriya, they became brāhmaṇas."

Raibhya, son of Sage Vatsara and grandson of Rishi Kashyapa had shudra children.

Kurma Purana Part 1: Chapter 19:4. From Vatsara were born Naidhruva and Raibhya of very great fame. The sons born from Raibhya were shudras who were the most excellent among the knower of vedas.

Yes. There are some examples. Children of King Rishabhdeva became Brahmana.

S.B. 5:4:13.In addition to these nineteen sons mentioned above, there were eighty-one younger ones, all born of Ṛṣabhadeva and Jayantī. According to the order of their father, they became well-cultured, well-behaved, very pure in their activities and expert in Vedic knowledge and the performance of Vedic rituals. Thus they all became perfectly qualified brāhmaṇas.

Descendants of King Dhrshta became Brahmanas.

S.B. 9:2:17.Manu also had a son known as Dhṛṣṭa, from whom another sect of kṣatriyas was generated, but although they were born of one who had the qualities of a kṣatriya, they became brāhmaṇas."

Raibhya, son of Sage Vatsara and grandson of Rishi Kashyapa had shudra children.

Kurma Purana Part 1: Chapter 19:4. From Vatsara were born Naidhruva and Raibhya of very great fame. The sons born from Raibhya were Shudras who were the most excellent among the knower of Vedas.