In-phase　coherent　vertical　cavity　surface　emitting　laser　(VCSEL)　arrays　have　desirable　properties　for　high-brightness　laser　applications.　We　employ　mutual　injection　feedback　modeling　of　ring　VCSEL　arrays　with　fractional　Talbot　cavity　to　select　their　supermodes.　An　analysis　of　the　effects　of　Talbot　cavity　lengths　on　engineering　the　coupling　coefficient　and　gain　threshold　for　in-phase　mode　operation　is　provided　through　the　overlapping　integrals　of　optical　field　distributions.　An　example　design　for　24-element　arrays　with　a　fractional　Talbot　cavity　is　presented,　and　the　in-phase　far-field　distribution　is　obtained.　This　provides　a　potential　method　for　fabricating　Bessel　Gaussian　beams　using　larger　ring　VCSEL　arrays.