May a paralegal sign a pleading by permission?

No, only an attorney or a party if not represented by an attorney may sign a pleading. The only person who may “sign by permission” for a licensed attorney is another licensed attorney. See T.R.C.P. 57. The signatures of attorneys or parties constitutes a certificate by them that they have read the pleading, that to the best of their knowledge, information and belief formed after reasonable inquiry the instrument is not groundless and brought in bad faith or groundless and brought for the purpose of harassment. See T.R.C.P. 13.