The first part of this verse is a quote of Exo 3:6. but, unusually, it is a paraphrase of the Greek of the Septuagint rather than a direct quote. Jesus leaves out the potentially confusing phrase "of thy father," which is addressed to Moses. He may have eliminated the "of thy father" phrase to clarify that the Divine's use of the present tense applied to the ancient patriarchs, who were long dead, rather than Moses's own father who could have been living.
Notice the emphasis that Jesus puts on the present tense of the Biblical quote spoken by God to Moses, but this verb tense is taken from the Greek Septuagint version, not the original Hebrew. In the original Hebrew, there is no verb, the pronoun "I" and "God" are equated by the construct form they share, which creates a combined word out of a series of words. Jesus is paraphrasing the Greek translation, where the tense of the verb "to be" is in the present tense. God does not say, "I was the God, of Abraham," despite the fact that the patriarchs died hundreds of years before Moses, but He is their God even though they seem dead from our perspective.
This paraphrasing is one more piece of evidence that Jesus taught in Greek (see article here), and the Greek of the synoptic Gospels are his actual recorded words. If Jesus's words always quoted the Septuagint exactly, as he does, for example, in Matthew 21:16 (Yes, haven't you read that out of the mouths), we might suspect that the Gospel writers corrected his quotes. But the fact that paraphrasing like this exists, shows that Jesus uses the phrasing of the Greek translation of the Old Testament as preachers today use their local translations.
There is also a lot of variation in the source Greek, especially in the last phrase among the different oldest versions of the Greek. It is a bit technical, but you can see those variations at this site. The biggest issue is the last line. In some versions it is "the God of dead," but it most it is "a god of dead." The later makes more sense to me. The original line from the Septuagint does not have the last line, but it say "a god" for second both Issac and Jacob.