A nonprofit foundation has been created in the wake of the Boston Marathon bombings to fund supplementary programs for the Police Department not covered by the town budget, as well as local community efforts, foundation organizers said. The Watertown Police Foundation Inc. will be headed up by Jay Darby, a lawyer who formerly worked on the Boston Police Foundation. The new foundation had collected about $50,000 as of last week, Darby said, and proceeds from “Watertown Strong” shirt sales also will be donated to the fund. Thousands of the shirts, which feature a Watertown Police Department insignia, have been sold nationwide in the last two weeks, organizers said. The shirts are available online at www.watertownpolicefoundation.org and at various retailers around Watertown and nearby communities, including Eastern Clothing, Francis Food Mart, Donohue’s Bar and Grill, and J&S Carpet Co. Contributions can also be sent to the Watertown Police Foundation Inc., 12 Robbins Road, Watertown, MA 02472. The foundation will use the donations to fund programs for Watertown officers focusing on issues such as suicide prevention and helping police through traumatic events. Darby said funds also could be used for the community, citing a Boston Police Foundation program that helps give local teens paid summer internships to keep them off the streets.