岐 is primarily used in place names such as 岐山 (Qishan, a historic area in Shaanxi) and as a variant of 歧, which means 'forked' or 'diverging'. Do not confuse with 奇 (qí, strange).
山 is the mountain radical and gives 岐 its grounding - the character names Mount Qi (岐山) in Shaanxi, the ancestral seat of the Zhou dynasty. By extension it means any forking mountain path, and metaphorically any branching or divergence.
支 gives the sound, drifting from zhī to qí. It also adds semantic flavour - 支 itself depicts a hand holding a branch, and 岐 means "branching, forking." Phonetic plus a clear semantic echo of "branch."
