In an Armenian text Michael Stone entitled "Concerning Adam, Eve, and the Incarnation," we find the following dialogue between Eve and the serpent in the three recensions of this text showing that at least some early Christians believed that God the Father experienced mortality like Jesus:
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3 Eve said, 'God said to us not to eat from the fruit of that tree, "lest you die." He said, "When you eat, at that very hour you (shall) go forth from this Garden, and you shall surely die."
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3 And Eve said, 'God said that we are not to eat of that fruit and "when you eat of it you shall surely die."'
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3 And the woman said, 'God commanded us not to eat of that. he said, "When you eat of that, you shall surely die."'
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4 The serpent spoke with Eve: '(That is) not so! God was a man like you. When he ate of the fruit of this tree he became God of all. Because of that God said to you not to eat, lest you become an equal god, like himself.'
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4 The serpent said, 'Because God was a man like you, when he ate this fruit he became God of all. Because of this matter he said, "Do not eat!" Lest you become god.'
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4 But the serpent said, '(That is) not so! Because God himself was a man like you when he ate of it, and he became God of all. Because of that he said not to eat of that, because you knew that when you eat of it, you will become a god, his equal. Because of that he said for you not to eat.'
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Source: Michael E. Stone, trans. Armenian Apocrypha Relating to Adam and Eve (Leiden: E.J. Brill, 1996), 25. Available on google books here.