Cases filed in federal court to force the government to decide a long-delayed application for immigration benefits are usually known as "Mandamus Cases" because they are brought under a law called the Mandamus Act (or Writ of Mandamus). But it's best to include in your complaint a claim under the Administrative Procedure Act (APA) as well. These two laws significantly overlap on delay cases. However, it's best to have both of them in your complaint because some courts have refused to act on just the Mandamus claim, saying an "alternate remedy" exists (meaning, there's another way to get what you want). These courts have said that the APA is an adequate "alternate remedy." Save yourself the trouble, risk and expense of an unnecessary dismissal and include both Mandamus and APA in your complaint.
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source https://www.reddit.com/r/immigration/comments/r7bum3/immigration_litigation_tip_when_fighting/