Delayed edit: Yes, apparently tidally-locked planets can have a surprisingly large magnetic field. Evidently the major reason for planetary fields is convection, not rotation. ([0] cites [1]) However, I believe there are also homopolar [2] generation effects due to the star and the planet's (tidally locked) rotation. [3] looked at fields caused by convection due to tidal flexing. [4] talks about magnetic interactions between stars and close planets.

[0] https://www.quora.com/How-does-the-magnetic-field-of-a-star-....

[1] “Energy flux determines magnetic field strength of planets and stars”, U. R. Christensen et al, Nature vol 457, pages 167–169

[2] https://en.wikipedia.org/wiki/Homopolar_generator#Astrophysi....

[3] https://exoplanets.nasa.gov/news/217/earth-like-exoplanets-m....

[4] https://www.youtube.com/watch?v=HjfOdjpNZHo (Talk by Evgenya Shkolnik, part of Short Course on Magnetic Fields: A Window to a Planet's Interior and Habitability at the Keck Institute for Space Studies at Caltech on August 12, 2013)

A tidally locked core would rotate once every 1.3 days, would it not?

[edit: Never mind. I think. Apparently it's rotation of two layers of core relative to each other that generates the field. However... since the plant is so close to its star, what would the effects be of a core rotating in a strong stellar field?]