You really can't go wrong with the Big List of Naughty Strings. The list is set up so that you can manually go through the text file list of strings that have caused issues in other inputs, or you can import it into test automation projects and use it there.
Some other things you might consider: if the text box is supposed to accept barcodes, does it do so by scanning them? If so, try scanning a QR code and see what happens. If you have a Square or other card swipe device, see what the field does if you swipe a card with a magnetic stripe (If you use a credit card, make sure you're not sending it anywhere or you're using test stock).
Hook your device up to a keyboard and lean on the keys or fall on the keys. What happens?
Simulate a pet walking across the device at the wrong time. What does that do?
I'd recommend this strategy:
- Start with the Big List of Naughty Strings; then
- Test sending input by non-standard methods (e.g. swipe, scanned, attached keyboard...)
Those two should be more than enough to find any serious issues the application has with input.
(disclaimer: I am not affiliated with the Big List in any way. I just find it an immensely valuable tool for testing)