If PPP Widget 2 works for you, PPP Widget 3 should work as well, maybe with a little speed improvement. Try it!

If you have a modem that DOESN'T work with PPP Widget 2, you should definitely try PPP Widget 3.

If you run into fundamental problems with PPP Widget 3, you can still come back to PPP Widget 2.

Use your 3G modem stick or your modem-enabled phone with your Wifi-only Android tablet for mobile Internet access, by using its USB host (OTG) feature or Bluetooth (with DUN devices). No additional kernel driver modules required.

This application is NOT guaranteed to work on every device combination because I obviously can't test every tablet or modem.
To increase your chances, READ and UNDERSTAND the full description, and check the requirement list!
Also, I only test on stock ROMs; custom ROMs can always provide USB modem support.

Be prepared to provide a detailed error report if things fail on your device. Don't just give a bad rating and write "Doesn't work" in the comment. That will neither help you nor anyone else.

REQUIREMENTS:

- Needs root access, with "SuperSU" app; other SU programs (like Kingroot) may cause problems
- For USB: Needs USB host connection (with OTG adapter)
- For USB: Needs a external USB power (modems draw more power than tablets can usually deliver)
- The modem or external phone to use must provide serial USB ports or the Bluetooth DUN profile and use the standard PPP protocol. Ask the manufacturer if unsure. Note that many newer 4G modems do NOT provide standard PPP ports.

This app is free. No ads. No data gathering.

It works with most devices on Android 4.x and 5.x with full network access, including Google Play downloads.
Note that the full network access may not work on all tablet models, due to modifications made to the Android system by manufacturers.

Keep in mind that this app is still young. If you get crashes, upload the bug report when asked, so that I can fix things. Better: report your problems at the PPP Widget forum. See link given in this FAQ page:
http://www.draisberghof.de/android/pppwidget2.html

Important: this is NOT a regular app - it is "widget only". You will NOT find its icon in the app menu. You have to place the WIDGET on a workspace manually.
Make sure you know how to access widgets on your device. It varies between manufacturers. Read the manual.

Also, this app uses the VPN feature of Android. However, this is the only way to create a network interface, there is no actual VPN.
As a consequence, real VPN will unfortunately not be possible over this connection.

Again, if your device combination does not work, write a report. Just complaining is not helpful. This app works closely to the device hardware which varies from model to model, and I can't test each and every modem or tablet out there, obviously.

Also, the USB host feature (OTG) is often not very robust.If your modem is not detected reliably, it may help to reboot the device once in a while, or change the ORDER of connecting OTG cable, hub, power and modem.

See http://www.draisberghof.de/android/pppwidget2.html for FAQs and feedback options.
No E-Mail please! You will just be redirected to the FAQs page and the support forum.

Details:

This widget enables Internet access over almost any USB or Bluetooth device with PPP modem capabilities, including many classic mobile phones (smartphones generally not included).

It is a complete rewrite of the previous "PPP Widget", with one of the main advantages being that additional kernel drivers are no longer required.
However, some Android devices have a "blacklist" for USB devices (like Sony Xperia Tablet Z) and may refuse to accept a range of possible USB accessories including modems.

Even if this app needs root access for building the connection, it does NOT alter any system files!
In case of severe and unusual problems just uninstall and reboot.