Mary undoubtedly belongs to one of the KAST or COST families of Frederick Co. MD; she may have eloped to the newly-established D.C. with Edward CLAY, but she returned to Frederick before moving to OH.
One Frederick Co. family was founded by Francis KAST (c.1707-bef.1782), whose will provided for one dau., Catherine (b. 17 Feb 1736/37), and two sons, George b. abt. 1745 and Jacob b. abt. 1749).There may have been other children who were not named.
A second Frederick Co. family was founded by Heinrich and Catherine KAST, who appear to have had children Frederick 1750, Thomas 1754, John 1755, and possibly Catherine 1763.
A third Frederick Co. line was founded by Johannes and Regina Barbara KAST, who bapt. children Daniel 1772, Catharina 1777, Johannes 1779, Catharina (again) 1782, and Maria Magdalena 1787.
Given the similarities among these naming patterns, it seems highly likely that these lines connect in an earlier generation.All of them adopted the anglicized "COST" in the next generation.Your Mary COST b. 1804 might be the dau. of almost any of the sons.You may learn more from German Reformed church records in Frederick Co. MD.