Continuity data is information about continuation applications that may have been filed based on a parent application. The USPTO
PAIR web site is available to the public and discloses information about patent applications that have published, as well as issued patents. Upon entering an issued patent number, patent application number, or publication number into
PAIR, you can view many of the prosecution details. If the patent of interest is a continuation application, or is the parent of a continuation application, there will be a clickable tab that reads “Continuity Data”. Clicking on the tab reveals the application numbers of any parent or child continuation applications.
Below is a screen shot from PAIR for U.S. Patent No. 5,861,542.

Clicking on the "Continuity Data" tab enables you to view continuity information. Below is the continuity data for U.S. Patent No. 5,861,542.

In this case, the patent has both "parent continuity data" and "child continuity data". You can then click on the application numbers for the parent and child applications acquire their status.