Gaura-Gadādhara Deities

I offer my respectful obeisances unto the internal potencies of the Lord, of whom Śrī Gadādhara Prabhu is the foremost.
(CC Adi 1.41)

Gadādhara Paṇḍita, the fourth branch, is described as an incarnation of the pleasure potency of Śrī Kṛṣṇa. No one, therefore, can equal him.
PURPORT
In the Gaura-gaṇoddeśa-dīpikā (147-53) it is stated, “The pleasure potency of Śrī Kṛṣṇa formerly known as Vṛndāvaneśvarī is now personified in the form of Śrī Gadādhara Paṇḍita in the pastimes of Lord Caitanya Mahāprabhu.” Śrī Svarūpa Dāmodara Gosvāmī has pointed out that in the shape of Lakṣmī, the pleasure potency of Kṛṣṇa, she was formerly very dear to the Lord as Śyāmasundara-vallabhā. The same Śyāmasundara-vallabhā was present in Lord Caitanya’s pastimes as Gadādhara Paṇḍita. Formerly, as Lalitā-sakhī, she was always devoted to Śrīmatī Rādhārāṇī. Thus Gadādhara Paṇḍita is simultaneously an incarnation of Śrīmatī Rādhārāṇī and Lalitā-sakhī. In the Twelfth Chapter of this part of the Caitanya-caritāmṛta there is a description of the descendants or disciplic succession of Gadādhara Paṇḍita.
(CC Adi 10.15)

Lord Śrī Caitanya Mahāprabhu is the Supreme Lord, and Nityānanda Prabhu and Advaita Prabhu are manifestations of the Supreme Lord. All of Them are viṣṇu-tattva, the Supreme, and are therefore worshipable by the living entities. Although the other two tattvas within the category of Pañca-tattva—namely, śakti-tattva and jīva-tattva, represented by Gadādhara and Śrīvāsa—are worshipers of the Supreme Lord, they are in the same category because they eternally engage in the transcendental loving service of the Lord.
(CC Adi 7.15 purport)

No one can describe the characteristics and ecstatic love of Gadādhara Paṇḍita. Therefore another name for Śrī Caitanya Mahāprabhu is Gadādhara-prāṇanātha, "the life and soul of Gadādhara Paṇḍita."
(CC Antya 7.163)

Gadādhara love for Mahaprabhu

Gadādhara Paṇḍita is celebrated all over the world for his gentle behavior, his brahminical attributes and his steady love for Śrī Caitanya Mahāprabhu.
(CC Antya 7.166)

Although He returned home, He did not enjoy household pleasures. Rather, He constantly enjoyed transcendental bliss. The tears of love that flowed from His eyes were such that it appeared that the Ganges, which flows from His feet, was now flowing from His eyes. The only words the Lord spoke were, “Where is Kṛṣṇa? Where is Kṛṣṇa?” Even on inquiry, there was no other reply. When the Lord saw any devotee, He asked, “Where is Kṛṣṇa?” After speaking in this way, the Lord would cry profusely, and various persons would solace Him according to their ability. One day Gadādhara happily came before the Lord with some betel nuts in his hand. On seeing Gadādhara, the Lord asked, “Where is that blackish Kṛṣṇa, who is dressed in yellow cloth?”  All the devotees there felt as if their hearts were pierced on seeing the Lord’s intense longing. Everyone was perplexed about how to reply. Gadādhara anxiously replied, “Kṛṣṇa always resides within Your heart.” As soon as the Lord heard the words, “Kṛṣṇa is in Your heart,” He began to scratch at His chest with His fingernails. Gadādhara quickly caught the Lord’s hands and pacified Him with various words of solace. Gadādhara said, “Be patient, Kṛṣṇa will come now,” as mother Śacī looked on. Mother Śacī became very pleased with Gadādhara and thought, “I haven’t seen such an intelligent boy before.” “Out of fear, I cannot stand before Him. Yet how nicely this boy has consoled Him.” Mother Śacī said, “My dear boy, always remain with Him. Do not leave Him and go anywhere else.”
(Śrī Caitanya-bhāgavata, Madhya-khaṇḍa 2.197 – 2.211)

After hearing the appeal of Mukunda, Śrī Gaurasundara went to the residence of Gadādhara. Gadādhara respectfully offered his obeisances to the Lord, who said, “Listen to what I have to say. O Gadādhara, I will not remain at home. I will go out to search for Kṛṣṇa. I will certainly give up My śikhā and brāhmaṇa thread. After shaving My head, I will go wherever I please.”
On hearing that the Lord would give up His śikhā, Gadādhara felt as though he had been struck in the head by a thunderbolt. In distress, Gadādhara said, “O Lord, Your statement is quite puzzling. Are You saying that a gṛhastha cannot be a Vaiṣṇava and that one attains Kṛṣṇa by giving up his śikhā and brāhmaṇa thread? O Lord, is this the benefit of shaving one’s head? This is just Your opinion, it is not the opinion of the Vedas. How will You leave Your widowed mother? You will from the outset become responsible for Your mother’s death. She will certainly not survive if You leave, for You are the only one she has left, and You are her life and soul. Is the Supreme Lord not pleased if one stays at home? A householder is liked by everyone. Still, if You are pleased by shaving Your head, then leave if that is what You desire.”
In this way, the Lord personally informed His intimate devotees, “I will give up My śikhā and brāhmaṇa thread.”
(Śrī Caitanya-bhāgavata, Madhya-khaṇḍa 26.166 – 26.178)