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In the mid-19th century, the surname Ward was found in every county in Ireland and the present day Northern Ireland. Emigrants left from every county in Ireland looking for a better opportunity so there is no way to pinpoint where William was from and very few church records are available to provide supporting documentation.
Have you considered DNA testing? You would qualify for the Y-DNA test which tracks your pure paternal line but in my own experience you may want to consider the general DNA test which looks at all of your paternal and maternal lines.