Dickens wove so many mysteries into Little Dorrit that tracing out their solutions is something like sorting out the Circumlocution Office. The mystery of Amy Dorrit's mother is a "red herring"--the fact that Amy is born in prison to a high profile prison couple leaves little room for doubt about her parentage. The reader is led to believe that Mrs. Clennam has wronged Amy somehow; it even occurs to the reader that Amy might be the daughter of either elder Clennam, though how that might have happened is beyond even Dickens' ability to solve sticky plot problems with astonishing coincidences.
The astonishing coincidence at the heart of Little Dorrit is pretty convoluted even for Dickens. Amy is the ultimate heir to a legacy left by Arthur's uncle, who regrets his part in the death of Arthur's real mother, a singing colleague of Amy's uncle. The legacy would have fallen to a daughter of Amy's uncle, if Uncle Frederick had had a daughter; in a stretch of legal logic, the inheritance falls to a daughter of Frederick's brother--Amy's father. As the will specified a "youngest daughter," Amy becomes the legatee (rather than her older sister Fanny). The legacy comes to nothing because revealing its existence would solve for Arthur the mystery of his father's watch and the wrong done by the Clennams against himself and his real mother.
In an unexpected plot twist, the fortune that Mr. Dorrit inherits and which frees the Dorrits from Marshalsea is completely unrelated to the Clennams. Arthur's good fortune at the end, which allows Arthur to clear his debt and marry Amy, is a job offer from his former business partner, who has outsourced himself and his inventions overseas and away from the Circumlocution Office.