How many writings of those who were disciples of the first 12 apostles, plus Paul, are available today? There's no need to include Mark and Luke as their writings are included in the Bible.
The group you're referring to is known as the Apostolic Fathers. The exact number is unknown, because some writings cannot be dated precisely.
These writings we can say with some confidence are from the Apostolic Fathers:
- 1 Clement, a letter written by Clement of Rome, a disciple of Peter. He may also be the same Clement mentioned by Paul in Philippians 4:3. There is also a letter called 2 Clement, but it is generally believed to have been written by a later author.
- Polycarp's letter to the Philippians. Polycarp was a disciple of John, and a martyr in the early second century.
- Seven letters of Ignatius of Antioch, who was also martyred in the early second century. He was a friend of Polycarp and probably a disciple of John.
- Fragments of the writings of Papias of Hierapolis. Papias is known to have written five books, which were often quoted by later Christians. Papias' own writings have since been lost, but the quotes from them survive in later works. Papius was also a disciple of John.
- The Shepherd of Hermas was considered Scripture by some early Christians, and actually appears in some early copies of the New Testament. By later consensus it was excluded from the NT because it came from the second generation of Christians, not the first.
These writings may or may not belong to that generation:
- The Didache. The full Greek title translates to "The Teaching of the Twelve Apostles". Some scholars believe these teachings were collected by the first disciples of the apostles, but other scholars believe this was a later work.
- The Apology of Quadratus of Athens. Quadratus was the first Christian apologist. Unfortunately, like the works of Papias, Quadratus' apology survives only in fragments quoted by later writers.
- The Apology of Aristides. This was believed lost for many centuries, until a copy was found in 1889 in St. Catherine's Monastery on Mount Sinai.
- The Epistle of Barnabas, attributed to Barnabas who traveled with Paul. Most scholars believe this was actually written by someone else.
- The Disputation of Jason and Papiscus attributed to Aristo of Pella. Survives only in fragments.
- The Epistle to Diognetus. The letter is attributed to "Mathetes", meaning "Disciple". The author calls himself "a Disciple of Apostles", but does not otherwise identify himself.
- The Martyrdom of Polycarp, written by someone who knew Polycarp. Whether they were of the same generation, we can't be sure.