A story in the Bible where Jesus tested the faith of a sinner?

I'm looking for a story in the Bible where Jesus put a sinner's faith to the test. I originally heard this story during a Church sermon. It was nearly 4 years ago, and and I'm having trouble figuring out which book this verse could belong in. I'm not sure, but it begins with a person asking Jesus for his forgiveness... I think She was a Gentile. Jesus Christ rejected that. The lady claimed that she still believes that Jesus will still forgive Her mistakes, because of Jesus' love for the sinners. In the end, Jesus revealed that He was just testing Her. He then said that **because of her faith, she was forgiven**. I kept looking for that story in many places, yet it still yields similar results. Have you ever heard this story or something similar? Do you think this story exist?