Signs of a True Apostle

The signs of a true apostle were performed among you with utmost patience, with signs and wonders and mighty works. (2 Corinthians 12:12 ESV)

Last of all, as to one untimely born, he appeared also to me. (1 Corinthians 15:8 ESV)

The office of the Apostles were held by the Twelve and Paul.
The important qualities of the office of Apostles that do not any succession:

1. Chosen by Christ;
2. Eye-witnesses of Christ;
3. Writers of New Testament.

Taken from this website "Is God restoring the offices of apostle and prophet in the church today?":
There was also a spiritual gift of apostle (this is not to be confused with the office - they are separate). Among those who had the spiritual gift were James (1 Corinthians 15:7; Galatians 1:19), Barnabas (Acts 14:4, 14; 1 Corinthians 9:6), Andronicus and Junias (Romans 16:7), possibly Silas and Timothy (1 Thessalonians 1:1; 2:7), and Apollos (1 Corinthians 4:6, 9). This latter group had the gift of apostleship but not the apostolic "office" conferred upon the Twelve and Paul. Those who had the gift of apostle, then, were those who carried the gospel message with God's authority. The word "apostle" means "one sent as an authoritative delegate." This was true of those who held the office of Apostle (like Paul) and those who had the spiritual gift (like Apollos). Though there are men like this today, men who are sent by God to spread the gospel, it is best NOT to refer to them as apostles because of the confusion this causes since many are not aware of the two different uses of the term apostle.

Taken from this website "Apostles & Prophets":
Paul sometimes uses the term "apostle" in a broader sense for a messenger like a legate (2 Corinthians 8:23; they are called apostles of the church)", a non-technical term with a general meaning. There is a difference supported in scripture to be an apostle of the Lord, personally chosen and sent by him; and an apostle of the church, sent out by the body of believers. This broader usage made it possible to include others who would be considered false apostles, messengers (2 Corinthians11:14; Revelation 2:2). Paul also uses the word for a group of witnesses who had seen the risen Lord before him and had received a specific call to an apostleship. This group was larger than the Twelve.