Does macOS Ventura support Airport Time capsule Version 6.3.9?

The very newest TC is now seven years old.

Wi-Fi 5, IEEE 802.11a/b/g/n/ac

Other TCs are far older.

The version 6.3 was the end of the line for AirPort Express, of which the newest are eighteen years old.

Try it.

Wouldn’t expect much for network performance.

Had random ~fifteen second drop-outs with TC gear too, no errors shown, and replaced it all.

Even if it works, I’d start budgeting for replacements. Preferably something with Time Machine server support.

Pending the information I requested FYI the oldest TC I happen to have in daily use is a third generation model running version 7.8.1 and is compatible with Ventura.

If your model is older than that it may or may not be able to have its firmware updated.

But we need to know the model. Not its version.

Open AirPort Utility. Hold an option key while double-clicking the Time Capsule. Its model will appear in its Summary tab.

Which model is it?

Click Cancel when you're finished.

You need to determine the Time Capsule model. Is something preventing you from doing that?