persevere at something
to keep trying to do something. I will persevere at my studies and I'm sure I will succeed. Todd persevered at his job and got promoted in no time.
persevere in something
to persist in [doing] something. I will persevere in my efforts to win election. Kelly persevered in her studies and graduated with honors.
persevere with something
to continue to try to accomplish something. Do you really think it is wise to persevere with your plan? Sally persevered with her scheme to earn a million dollars.