Mark seems to be most directly alluding to his "tzitziyot", which all Jewish men were to wear:

[Num 15:38 HNV] Speak to the children of Yisra'el, and bid those who they make them tzitziyot in the borders of their garments throughout their generations, and that they put on the tzitzit of each border a cord of blue:
[Num 15:39 HNV] and it shall be to you for a tzitzit, that you may look on it, and remember all the mitzvot of the LORD, and do them; and that you not follow after your own heart and your own eyes, after which you use to play the prostitute;
The fact that Jews of the second temple period associated the clothing of the messiah with physical healing suggests to me that they did in fact associate his "fringes" with healing, per Malachi 4:2.
[Mar 6:56 HNV] Wherever he entered, into villages, or into cities, or into the country, they laid the sick in the marketplaces, and begged him that they might touch just the tzitzit of his garment; and as many as touched him were made well.
Actually, it should read “as many as touched IT were made well”! This in turn seems to ultimately be an allusion to this:
[Eze 44:19 KJV] And when they go forth into the utter court, even into the utter court to the people, they shall put off their garments wherein they ministered, and lay them in the holy chambers, and they shall put on other garments; and they shall not sanctify the people with their garments.
We know that Paul's clothing communicated healing as well:
[Act 19:11 ASV] And God wrought special miracles by the hands of Paul:
[Act 19:12 ASV] insomuch that unto the sick were carried away from his body handkerchiefs or aprons, and the diseases departed from them, and the evil spirits went out.