What is the earliest claim that Jesus Christ kept the law of Moses on behalf of others?

The idea that Christ fulfilled the Law of Moses and thus so do believers may be found at least as early as Thomas Aquinas (1225-1274) in his work Summa Theologica. To be clear, Aquinas quotes scripture, which of course sources some 1200 years earlier.

Now two things of every law is to make men righteous and virtuous, as was stated above (Q[92], A1): and consequently the end of the Old Law was the justification of men. The Law, however, could not accomplish this: but foreshadowed it by certain ceremonial actions, and promised it in words. And in this respect, the New Law fulfils the Old by justifying men through the power of Christ's Passion. This is what the Apostle says (Rom. 8:3,4): "What the Law could not do . . . God sending His own Son in the likeness of sinful flesh . . . hath condemned sin in the flesh, that the justification of the Law might be fulfilled in us." And in this respect, the New Law gives what the Old Law promised, according to 2 Cor. 1:20: "Whatever are the promises of God, in Him," i.e. in Christ, "they are 'Yea'." [*The Douay version reads thus: "All the promises of God are in Him, 'It is'."] Again, in this respect, it also fulfils what the Old Law foreshadowed. Hence it is written (Col. 2:17) concerning the ceremonial precepts that they were "a shadow of things to come, but the body is of Christ"; in other words, the reality is found in Christ. Wherefore the New Law is called the law of reality; whereas the Old Law is called the law of shadow or of figure.

Now Christ fulfilled the precepts of the Old Law both in His works and in His doctrine. -source-

In this quote, we find these things.

The end of the Old Law was the justification of men, but this could not be accomplished, except in the New Law of Christ, by which men are justified, in which are found the promises of God, in Him.

For Aquinas, the New Law is called the law of faith, in so far as its pre-eminence is derived from that very grace which is given inwardly to believers, and for this reason is called the grace of faith. -source-

I answer that, "Each thing appears to be that which preponderates in it," as the Philosopher states (Ethic. ix, 8). Now that which is preponderant in the law of the New Testament, and whereon all its efficacy is based, is the grace of the Holy Ghost, which is given through faith in Christ. Consequently the New Law is chiefly the grace itself of the Holy Ghost, which is given to those who believe in Christ. This is manifestly stated by the Apostle who says (Romans 3:27): "Where is . . . thy boasting? It is excluded. By what law? Of works? No, but by the law of faith": for he calls the grace itself of faith "a law." And still more clearly it is written (Romans 8:2): "The law of the spirit of life, in Christ Jesus, hath delivered me from the law of sin and of death." Hence Augustine says (De Spir. et Lit. xxiv) that "as the law of deeds was written on tables of stone, so is the law of faith inscribed on the hearts of the faithful": and elsewhere, in the same book (xxi): "What else are the Divine laws written by God Himself on our hearts, but the very presence of His Holy Spirit?" -source-

I suspect there are others who make the same claims (the Old Law is fulfilled in Christ and imputed to man), but time does not permit a more thorough search.

This is the earliest extra-biblical clear statement I have found so far.

Christ therefore ransomed from the curse of the law those who being subject to it, had been unable to keep its enactments. And in what way did He ransom them? By fulfilling it. And to put it in another way: in order that He might expiate the guilt of Adam’s transgression, He showed Himself obedient and submissive in every respect to God the Father in our stead… - St. Cyril of Alexandria (378 – 444 AD) – Commentary on Luke

1 Peter 3:18 "For Christ also suffered once for sins, the righteous for the unrighteous, that he might bring us to God, being put to death in the flesh but made alive in the spirit," is a more indirect declaration wherein one must make the leap that he was righteous by keeping the Law.