The first personal expansion is Sankarsana, and the others are incarnations like the fish incarnation. Sankarsana is an expansion of the Purusa, or Visnu

Expressions researched:
"The first personal expansion is Saṅkarṣaṇa, and the others are incarnations like the fish incarnation. Saṅkarṣaṇa is an expansion of the Puruṣa, or Viṣṇu"

Sri Caitanya-caritamrta

CC Madhya-lila

“The first personal expansion is Saṅkarṣaṇa, and the others are incarnations like the fish incarnation. Saṅkarṣaṇa is an expansion of the Puruṣa, or Viṣṇu. The incarnations such as Matsya, the fish incarnation, appear in different yugas for specific pastimes."

CC Madhya 20.244, Translation and Purport

“The first personal expansion is Saṅkarṣaṇa, and the others are incarnations like the fish incarnation. Saṅkarṣaṇa is an expansion of the Puruṣa, or Viṣṇu. The incarnations such as Matsya, the fish incarnation, appear in different yugas for specific pastimes."

The puruṣa-avatāras are the Lords of the universal creation. These are Kāraṇodakaśāyī Viṣṇu, Garbhodakaśāyī Viṣṇu and Kṣīrodakaśāyī Viṣṇu. There are also līlā-avatāras, and these include (1) Catuḥsana, or the four Kumāras, (2) Nārada, (3) Varāha, (4) Matsya, (5) Yajña, (6) Nara-Nārāyaṇa, (7) Kārdami Kapila, (8) Dattātreya, (9) Hayaśīrṣā, (10) Haṁsa, (11) Dhruvapriya, or Pṛśnigarbha, (12) Ṛṣabha, (13) Pṛthu, (14) Nṛsiṁha, (15) Kūrma, (16) Dhanvantari, (17) Mohinī, (18) Vāmana, (19) Bhārgava Paraśurāma, (20) Rāghavendra, (21) Vyāsa, (22) Pralambāri Balarāma, (23) Kṛṣṇa, (24) Buddha and (25) Kalki.

These twenty-five Personalities of Godhead are known as līlā-avatāras. Because they appear in each day of Brahmā, or in each kalpa (millennium), they are sometimes known as kalpa-avatāras. Of these incarnations, Haṁsa and Mohinī are neither permanent nor very well known, but They are listed among the prābhava-avatāras. Kapila, Dattātreya, Ṛṣabha, Dhanvantari and Vyāsa are eternally situated and very widely known. They are also counted among the prābhava incarnations. Kūrma, Matsya, Nārāyaṇa, Varāha, Hayagrīva, Pṛśnigarbha and Baladeva, the killer of Pralambāsura, are counted among the vaibhava-avatāras.