Ephesians 1:1

Paul, an apostle of Christ Jesus through the will of God, to the holy ones who are at Ephesus, even the faithful in Christ Jesus:
- Ephesians 1:1

Paul, an apostle of Christ Jesus - The word "apostle" literally means "sent one" and although it can be used in a political sense, it's use in the New Testament is more geared toward the Jewish religious sense. If there was a prominent Rabbi, he sometimes would send out some of his students as apostles to teach others the teachings he had taught them. This makes sense when we see Jesus pick 12 apostles in the Gospels to carry on his teachings. False teachers were saying Paul was not an apostle of Christ like the other apostles.   Paul responds by saying that he is a direct apostle of the Jesus Christ.

Galatians 1:1
Paul, an apostle (not from men, neither through man, but through Jesus Christ , and God the Father,who raised him from the dead),

Luke shows that Paul was commissioned by Jesus to be an apostle. On the road to Damascus, Jesus appears to Paul and says:

Acts 26:16-18
But arise, and stand on your feet, for I have appeared to you for this purpose: to appoint you a servant and a witness both of the things which you have seen, and of the things which I will reveal to you; delivering you from the people, and from the Gentiles, to whom I send you, to open their eyes, that they may turn from darkness to light and from the power of Satan to God, that they may receive remission of sins and an inheritance among those who are sanctified by faith in me.

When a Rabbi would send out an apostle, he would give them a letter proving their apostleship. Paul describes his "letter" as well:

2 Corinthians 3:2-3
You are our letter, written in our hearts, known and read by all men; being revealed that you are a letter of Christ, served by us, written not with ink, but with the Spirit of the living God; not in tablets of stone, but in tablets that are hearts of flesh.

The false teachers were saying that Paul was not preaching the correct Gospel because he only taught the Way of the Spirit and not the Way of the Flesh. Paul writes about teaching the gospel he learned from Jesus in Eph. 3:3 and elsewhere:

Galations 1:11-12
But I make known to you, brothers, concerning the Good News which was preached by me, that it is not according to man. For neither did I receive it from man, nor was I taught it, but it came to me through revelation of Jesus Christ.

Paul mentions that he had not studied under any of the apostles:

Galatians 1:18-19
Then after three years I went up to Jerusalem to visit Peter, and stayed with him fifteen days. But of the other apostles I saw no one, except James, the Lord's brother.

When he did meet with the apostles, they had no problems with the Gospel he preached:

Galations 2:2
I went up by revelation, and I laid before them the Good News which I preach among the Gentiles, but privately before those who were respected, for fear that I might be running, or had run, in vain. But not even Titus, who was with me, being a Greek, was compelled to be circumcised.

through the will of God - Paul defends his apostleship for almost the entire chapter in 1 Corinthians 9. He also talks about how he preaches the gospel not out of his own will:

1 Corinthians 9:16-17
For if I preach the Good News, I have nothing to boast about; for necessity is laid on me; but woe is to me, if I don't preach the Good News. For if I do this of my own will, I have a reward. But if not of my own will, I have a stewardship entrusted to me.

to the holy ones who are at Ephesus, even the faithful in Christ Jesus - Paul writes to the holy ones. The false teachers were saying that those who had faith in Christ were not holy ones. Paul corrects this by saying "even the faithful in Christ Jesus"