Who exactly is resurrected and reigns in the millennial city in premillennialisim?

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Both dispensational and historic premillennialists hold that all Christians who died or were raptured prior to the beginning of the millennium will reign with Christ during it.

One standard dispensational commentary, the Moody Bible Commentary, describes two groups of people that will reign with Christ in its treatment of Revelation 20:

Verses 4a-b refer to the Church saints resurrected at the rapture, who rule and reign with Jesus. After this, John saw the resurrection of another group, the tribulation saints, those who had been beheaded (martyred) during the tribulation for resisting idolatry. "They came to life" means that their bodies had now been joined, through resurrection, to their souls that were already in heaven. They also "reigned with Christ."

This commentary views both of these groups as part of the "first resurrection":

The phrase "this is the first resurrection" (v. 5b) summarizes the experience of all believers, including those martyred in the tribulation.

Prominent Dispensationalist John MacArthur says in a sermon on this passage:

So you've got resurrected Old Testament saints, you've got resurrected saints who followed Jesus during His lifetime, you've got resurrected New Testament saints, and now you've got resurrected Tribulation saints and it's all the resurrected saints who reign. They came to life and reigned with Christ a thousand years. [emphasis added]

Historic premillennialists like Wayne Grudem see things similarly.

After that time of tribulation at the end of the church age, Christ will return to earth to establish a millennial kingdom. When he comes back, believers who have died will be raised from the dead, their bodies will be reunited with their spirits, and these believers will reign with Christ on earth for one thousand years. [...] The believers who have been raised from the dead, and those who were on the earth when Christ returns, will receive glorified resurrection bodies that will never die, and in these resurrection bodies they will live on the earth and reign with Christ. [bold added]

Given the disagreement over the finer points of interpretation of Revelation, it's quite likely that some espousing premillennialism will diverge from this position. But it's significant that these prominent proponents of their respective eschatological views agree that all dead and raptured Christians will reign during the millennium.

Grudem's summary is found in his Systematic Theology, chapter 55, page 1112. The notes from Moody Bible Commentary are found in the section on Revelation 20:4–6. I cleaned up the formatting and made several unmarked omissions of parenthetical remarks when quoting from the latter.