Since the clouds in the sky were mildly thundering and showering, Ananta-naga, an expansion of the SP of Godhead (Krsna), followed Vasudeva, beginning from the door, with hoods expanded to protect Vasudeva & the transcendental child - SB 10.3.48-49

Expressions researched:
"Since the clouds in the sky were mildly thundering and showering, Ananta-naga, an expansion of the Supreme Personality of Godhead, followed Vasudeva, beginning from the door, with hoods expanded to protect Vasudeva and the transcendental child"

SB Canto 10.1 to 10.13

Since the clouds in the sky were mildly thundering and showering, Ananta-nāga, an expansion of the Supreme Personality of Godhead, followed Vasudeva, beginning from the door, with hoods expanded to protect Vasudeva and the transcendental child.

SB 10.3.48-49, Translation and Purport:

By the influence of Yogamāyā, all the doorkeepers fell fast asleep, their senses unable to work, and the other inhabitants of the house also fell deeply asleep. When the sun rises, the darkness automatically disappears; similarly, when Vasudeva appeared, the closed doors, which were strongly pinned with iron and locked with iron chains, opened automatically. Since the clouds in the sky were mildly thundering and showering, Ananta-nāga, an expansion of the Supreme Personality of Godhead, followed Vasudeva, beginning from the door, with hoods expanded to protect Vasudeva and the transcendental child.

Śeṣa-nāga is an expansion of the Supreme Personality of Godhead whose business is to serve the Lord with all necessary paraphernalia. When Vasudeva was carrying the child, Śeṣa-nāga came to serve the Lord and protect Him from the mild showers of rain.