Is there any way to upgrade my jailbroken iPad to a higher jailbreakable iOS? I have a jailbroken fourth-generation iPad running iOS 6.1.3.  I'd like to upgrade it to some higher iOS, but not the latest iOS (10.3.3 or 11), since no jailbreak exists for that.  My question is, is there anyway I can upgrade my iPad to an iOS for which a jailbreak exists?

I think the short answer to my question is "blobs".  In the old days there was just SHSH blobs, but now the terminology is more complicated, like SHSH2, ApTicket, and TSS.  In any case, how do I check if I have the right kind of blobs  to do the kind of upgrade I want?  Are they still saved in Cydia like in the old days, or what?
Short answer

No, unfortunately not.

Explanation

Without any manually saved SHSH blobs for your desired version of iOS and your device you cannot upgrade to this version of iOS.

Check https://api.ineal.me/tss/status to see which firmware versions are currently being signed by Apple.

As of today Apple signs only this iPad 4 (iPad 3,4; 3,5; 3,6) firmware:

10.3.3    14G60

Additional Resources

You may check whether there are SHSH2 blobs available for your device:

https://tsssaver.1conan.com

You can get you ECID by


Lauching iTunes
Connecting your device using a Lightning cable to your computer
Selecting your device in iTunes
Clicking the serial number twice