…in order that I may attain to the ressurection of the dead.
What is the resurrection of the dead that Paul is hoping to attain through fellowship of Christ’s sufferings and knowledge of Him?
The study note in the New World Translation offers some clarity to Paul's statement:
the earlier resurrection: Many translations simply use the word “resurrection.” However, Paul does not use the usual Greek word for resurrection (a·naʹsta·sis), but he uses a closely related word (e·xa·naʹsta·sis; lit., “out-resurrection,” Kingdom Interlinear) that occurs only here in the Christian Greek Scriptures. For this reason, a number of scholars comment that this expression refers to a special resurrection. The term was used in classical Greek literature to refer to getting up early in the morning. Paul’s use of this specialized word suggests that he has in mind a resurrection that comes early in the stream of time (1Co 15:23; 1Th 4:16), before the general resurrection of the dead to life on earth (Joh 5:28, 29; Ac 24:15). This early resurrection is also called “the first resurrection,” and it involves the raising of Christ’s spirit-anointed followers to life in heaven.—Re 20:4-6.
For additional information on "the first resurrection" mentioned in Revelation 20:5, 6, see the subheading "First resurrection" in the Insight on the Scriptures.
[All scripture quotations from the New World Translation of the Holy Scriptures (Study Edition)]
Paul's concept of the resurrection of the dead was surely worked out in relationship to his training as a Pharisee, said in Acts to have been done "at the feet of Gamaliel," (Acts 22:3) the greatest rabbinical authority of that age. The earliest written sources of rabbincal doctrine concerning the resurrection are mostly from the next century and later. The Jewish Encyclopedia summarizes:
By means of the "dew of resurrection" (see Dew) the dead, will be aroused from their sleep... As to the question, Who will be raised from death? the answers given vary greatly in rabbinical literature... according to R. Abbahu, only the just (Ta'an. 7a); some mention especially the martyrs (Yalḳ. ii. 431, after Tanḥuma)... According to R. Jonathan (Pirḳe R. El. xxxiv.), the resurrection will be universal, but after judgment the wicked will die a second death and forever, whereas the just will be granted life everlasting (comp. Yalḳ. ii. 428, 499). The same difference of view prevails also among the New Testament writers; at times only "the resurrection of the just" is spoken of (Luke xiv. 14, xx. 35); at other times "the resurrection of the dead" in general is mentioned (John v. 29; Acts xxiv. 15; Rev. xx. 45).
Paul combines the concept of the resurrection of the dead, which for some of the rabbis included the wicked, with the idea of the resurrection of the just. But for Paul, righteousness is attained only through faith in Christ's atoning death. Thus he says immediately before the OP's verse that:
I count all things to be loss in view of the surpassing value of knowing Christ Jesus my Lord, for whom I have suffered the loss of all things, and count them mere rubbish, so that I may gain Christ, and may be found in Him, not having a righteousness of my own derived from the Law, but that which is through faith in Christ, the righteousness which comes from God on the basis of faith, that I may know Him and the power of His resurrection.
We may reject the idea that Paul speaks of a general resurrection here, since he ties the idea to knowledge of Christ. The mention of sufferings is consistent with the rabbinic idea that martyrs in particular hold a place of honor in "the world to come." This derives in part from 2 Maccabees, where the Jewish martyrs under Antiochus IV are especially praised. It may indicate that Paul foresaw his own martyrdom, although it could also refer the sufferings he had already experienced in preaching the Gospel.
The resurrection of the dead that Paul refers to is thus synonymous with the resurrection of the just, understood to mean those who have attained justification through faith in Christ.