As a rule of thumb anyone closer than a 3c will share DNA with you and the child of a half 1c is well within that range, the expected shared dna in such a case would be 62-469cM. How much DNA do you share with this person and do you other shared matches with them?
The first step when dna results come through is to group matches together, many will mention the Leeds method but basic grouping is sufficient. If a batch of matches share dna with each other and also with you that is a group and you will all descend from a common ancestor.
Build the trees of your matches using traditional records to see where the trees intersect, if they don't intersect it suggests there's something amiss in the records, perhaps a child born to an unknown partner, earlier/later marriage or out of wedlock but when registered the details provided were fictitious and simply an attempt to hide the truth. At that point expanding the search and looking more deeply at shared matches really comes into play.