The Foundling by Amy D’Orazio

The Foundling is the love story of Miss Frederica Richmond, left alone to grow to adulthood in an orphanage after her parents’ death. It is the third book in the Rags to Richmonds series co-authored by Jessie Lewis and Amy D’Orazio.
MISS FREDERICA CHILD KNOWS EXACTLY WHO SHE IS. She has always known, for as long as she can remember, that she is the granddaughter of the Earl of Tipton, from whom her father had been estranged prior to his death. But she does not begrudge the life of luxury she never had; her work at the Taverstock Orphanage, creating a sort of adoptive family, is all the reward she desires.

ALAS, JUST AS SHE BECOMES AN ADULT, her contentment is due to be shattered. A new patron of the orphanage—the handsome, young, and recently bereaved Duke of Penrith—discovers her secret and reveals her whereabouts to her estranged family. The reunion is a surprise to everyone, but in one thing the Richmonds are sure: Frederica must return to her family and the life she is due as the granddaughter of nobility.