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The story of Moses is in the Book of Exodus in the Bible and begins in Chapter two. It is a fascinating story and the answer to your question is addressed in:
Exodus 2:10 KJVΒ Β And the child grew, and she brought him unto Pharaoh's daughter, and he became her son. And she called his name Moses: and she said, Because I drew him out of the water.
We do not know whether the eventual Pharaoh you asked about was a natural son of Pharaoh's daughter or not, but being the assumed son of Pharaoh's daughter; Moses would have grown up in the Palace. If the second Pharaoh was the natural son of Pharaoh's daughter, he would have been natural ascendant to the throne.
It is also probable that He and Moses would have been considered as brothers.
Other than those considerations the Bible shows Aaron and Meriam to be the only siblings of Moses.
Hope this helps.
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The daughter of Pharaoh who retrieved Moses from the basket in the Nile and adopted him was Hatshepsut. Hatshepsut had no sons and only one daughter called Neferura. Hatshepsut's husband was Thutmose II who had one son by one of his lesser marriages who became Thutmose III.
The difficulty of the Pharaohs of the 18th dynasty to have sons, especially by the Great Royal Wives may have been a consequence of interbreeding. The Great Royal Wives were often half-sisters or even full sisters. Hatshepsut needed a son, even if an adopted son, in order that when her husband, as Pharaoh, died, then her son would become Pharaoh rather than the son of a lesser wife. If her son became Pharaoh then her position and power would be maintained. We see then her need to adopt a son which providentially was Moses.
So Thutmose III was Moses's half-brother. Thutmose III father was Moses's adoptive father.
When Thutmose II died in 1504 Moses would have been 22 years old and Thutmose III would have been perhaps as young as 2 years old. So Moses claim to the throne was better because he was an older son. But what really made his claim better was that he was the (only) son of the Great Royal Marriage. The statement of Hebrews 11:24-26 is borne out by the historical data, the most realistic reason Moses did not become Pharaoh himself is that he refused, and furthermore he would have refused greatly to the annoyance of, and under great pressure from, his mother Hatshepsut. Her plans to maintain her power were completely messed up by Moses's refusal.