In my family it has always been said that we have Jewish ancestors, could I apply for Portuguese nationality by Sephardic origin?

Yes, DECREE LAW No. 30-A/2015 allows to obtain Portuguese nationality to all persons who prove to be descendants of Sephardic families. In SEFAR UNIVERSAL we have an extraordinary team of genealogists and historians who will facilitate your research work and will manage to connect you with your Jewish ancestry if, as indeed you say, you descend from Jewish families.
Do not hesitate to order your genealogical feasibility study through the registration on our page www.sefaruniversal.com. From our organization, genealogists will carry out a preliminary study to check its viability and, if it is positive, to start the procedure.