Theophylact of Ohrid

So much so that they even desired to touch the hem of His garment, and indeed, when they did so, they were healed. You also, O reader, touch the edge of Christ's garment, which is the end of His sojourning in the flesh. For if you believe that He ascended, you will be saved. The garment means His flesh, and its hem, the end of His life on earth.

Commentary on Matthew ↗

Jerome

And all who were sick approached him, and they begged him to touch the fringe of his garment. And whoever touched it, they were healed. But those who were sick should not touch the body of Jesus or the entire garment, but only the edge of the fringe, and whoever touched it, they would be healed. Understand the fringe of his garment, or at least understand this commandment: whoever breaks it will be considered the least in the kingdom of heaven (Above, III). …

Commentary on Matthew ↗

Hilary of Poitiers

Many things came in the way that, after the gathering of five thousand men who were filled to satiety, dampened our effort to give a proper account. Our understanding on this point, however, remains the same. The time of the law was over, and five thousand men were brought into the church from lsrael. The believing people now hastened from the law, saved through their faith. They offered to God the remaining persons among them who were feeble and ill. …

Commentary on Matthew 14.19 ↗

Thomas Aquinas

Likewise, devotion is also demonstrated, because they not only asked that he lay hands on them, but they only besought him that they might touch but the hem of his garment. By the hem is signified the least commandments, or the flesh of Christ, or the sacrament of Baptism. And as many as touched, namely through faith, were made whole. Hence Mark 16:16: he that believes and is baptized shall be saved.

Commentary on Matthew ↗