John Chrysostom

What is this; "fellow-heirs, and fellow-partakers of the promise, and fellow-members of the body?" This last is the great thing, that they should be one body; this exceeding closeness of relation to Him. For that they were to be called indeed, that they knew, but that it was so great, as yet they knew not. This therefore he calls the mystery. "Of the promise." The Israelites were partakers, and the Gentiles also were fellow-partakers of the promise of God. …

Homily on Ephesians 6 ↗

Theophylact of Ohrid

The mystery consists in the fact that the Gentiles became fellow heirs and fellow partakers of the promise of Israel. For the Israelites partook in the promise as a holy people; and the Gentiles, formerly unclean, became partakers with them of the same promise, but in what way? "In Christ," that is, through faith in Christ, which reached them through the Gospel. …

Commentary on Ephesians ↗

Jerome

Now the meaning of fellow heirs is this: Just as there are many members in one body … and these, though in one body, have their differences and feel their own joy and grief in turn, so those who have believed in Christ, even if they have different gifts, are bonded together in the one body of Christ.

Commentary on Ephesians 3:5-7 ↗

Thomas Aquinas

Consequently, when he states that the Gentiles should be fellow heirs, he makes known what the sacrament is. In reference to it, it should be recognized that the Jews enjoyed three prerogatives with respect to the Gentiles. They had the promised inheritance: "For not through the law was the promise to Abraham or to his seed, that he should be heir of the world; but through the justice of faith" (Rom. 4:13); "The Lord is the portion of my inheritance" (Ps. 15:5). …

Commentary on Ephesians ↗