The dictionary term for paternal is "fatherly or from the father's side of the family."
A family tree will typically contain the father's (paternal) and the mother's (maternal) living relatives and also ancestors for each person included in the family tree.
Beginning the Search
When making a paternal family tree or the paternal branch of a larger work of genealogy, start with the most recent father. Your own father would be a starting point for your own paternal family tree.
Follow the Paternal Lineage
If the most recent father begins a branch of the family tree, his parents will come next. Include both parents of the person for whom the tree is being created. Paternal family trees track the entire lineage of the subject, not just his male ancestors.
From Any Starting Point
It isn't uncommon for genealogy searchers to begin with an ancestor from many generations ago, then move forward to the future. This type of search is often done when a person is searching for her own connection to a particular person from history or simply from the family's ancestry. For example, if it is known that a man came to Ellis Island in a certain year, a searcher may look from that year forward to find out if there is a family connection.