I am somewhat astonished/puzzled that the question concerning the God who Jesus Christ worshipped is rarely raised. And yet, I am convinced that the answer to this question is foundational to understanding who the true God is.
I would like to begin my exploration into the answer of this question by quoting an exchange Jesus had with a Pharisee/scribe:
And one of the scribes came, and having heard them reasoning together, and perceiving that he had answered them well, asked him, Which is the first commandment of all?
And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one Lord:
And thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind, and with all thy strength: this is the first commandment.
And the second is like, namely this, Thou shalt love thy neighbour as thyself. There is none other commandment greater than these.
And the scribe said unto him, Well, Master, thou hast said the truth: for there is one God; and there is none other but he:
And to love him with all the heart, and with all the understanding, and with all the soul, and with all the strength, and to love his neighbour as himself, is more than all whole burnt offerings and sacrifices.
And when Jesus saw that he answered discreetly, he said unto him, Thou art not far from the kingdom of God. And no man after that durst ask him any question. (Mark 12:28-34 - KJV; see also Matt. 22:34-40; Luke 10:25-28.)
I am going to suggest that within the above dialogue, we have the very essence of what constitutes true faith; the true faith that forms the foundation of Judaism, Christianity and Islam. The essence is this: first, belief in and love of the One God; and second, love of your neighbor as yourself.
Now, this One God is the God who Jesus Christ worshipped, "the God and Father" of Jesus Christ, the God who he addressed as "my God", the God of "Abraham, Isaac and Jacob". This One God is the source of everything else that exists (including the Son of God and the Holy Spirit).
Concerning the love of your neighbor as yourself, apart from the love of God, there is no greater commandment. If one loves their neighbor as oneself, "all the Law is fulfilled" (Gal. 5:14; see also James 2:8), and one will "inherit eternal life" (Luke 10:25-28).
Jesus Christ loved the One God with all his heart, and with all his soul, and with all his mind, and with all his strength; and he loved his neighbor as himself. He taught us that all mankind should follow his example, and that those who do so will inherit eternal life, the kingdom of God.
Who am I to second guess his example and exhortation...
Grace and peace,