Tatpurusha is not a God. "Tat" (तत्) literally means "that".
"Purusha" is a concept referring to the Cosmic Self, Cosmic Consciousness, or the Universal Principle. This concept came about from the Purusha Suktam when it referred to a cosmic man who was sacrificed by the gods to create all life. In Yoga philosophy, Purusha also references the true Self - the realization of which is a goal of yoga practice as defined in The Yoga Sutras of Patanjali. It is also the ultimate goal of all Vedic practices and Vedantic philosophy, examination and inquiry.
Shwetashvatara Upanishad Adhyaya III defines Purusha as such:
mahān prabhur vai puruṣaḥ sattvasyaiṣa pravartakaḥ |
sunirmalām imāṃ prāptim īśāno jyotir avyayaḥ || (3.12)
That person (purusha) is the great lord; he is the mover of
existence, he possesses that purest power of reaching everything, he
is light, he is undecaying.
aṅguṣṭhamātraḥ puruṣo 'ntarātmā sadā janānāṃ hṛdaye saṃniviṣṭaḥ |
hṛdā manīṣā manasābhikḷpto ya etad vidur amṛtās te bhavanti || (3.13)
The person (purusha), not larger than a thumb, dwelling within,
always dwelling in the heart of man, is perceived by the heart, the
thought, the mind: they who know it become immortal.
sahasraśīrṣā puruṣaḥ sahasrākṣaḥ sahasrapāt |
sa bhūmiṃ viśvato vṛtvā atyatiṣṭhad daśāṅgulam || (3.14)
The person (purusha) with a thousand heads, a thousand eyes, a
thousand feet, having compassed the earth on every side, extends
beyond it by ten fingers’ breadth.
puruṣa evedaṃ sarvaṃ yad bhūtaṃ yac ca bhavyam |
utāmrtatvasyeśāno yad annenātirohati || (3.15)
That person alone (purusha) is all this, what has been and what
will be; he is also the lord of immortality; he is whatever grows by
Tatpurusha (तत्पुरुष) is also one of the eleven emanations of Rudra, according to the Roopamandana (a text of Shilpa shastra). Other emanations are : Ishana, Aghora, Vamadeva, Sadyojatha, Mrityunjaya, Kiranaksha, Srikanta, Abhirbhudhya, Bahurupa and Tryambaka.
So ultimately, Tatpurusha refers to the cosmic self in all Jivas.
Therefore the Shanmukha (Subhramanya) Gayatri mantra translates to
"Om, Let me meditate on that (tat) great male (purusha),
Oh, commander in chief, give me higher intellect,
And let the six faced one illuminate my mind."