Felpham runs one primary and one secondary inside the village. Bishop Tufnell Church of England Primary School covers the early years. Felpham Community College handles the secondary years. A wider ring of schools sits next door in Bognor Regis. What this brief does not carry is an Ofsted grade for any of them, so the version of the question that asks "which one is best" does not have an answer on this page.
Naming a school is not the same as getting a place at it. Felpham Community College is the secondary inside the village, but the catchment line is set by the local education authority and depends on the year, distance from the gate, sibling status, and that year's applicant pool. Bishop Tufnell on the primary side runs the same logic. Living in Felpham puts you closer to both doors than living in Barnham or Bognor proper does. Living closer to the door is not the same thing as a place at the door, and the same is true at every named school in the area.
For families who don't land a Bishop Tufnell place, the nearest primary alternatives sit a short drive away in greater Bognor Regis. The brief's named primary list includes Barnham Primary School, Bartons Primary School, Bersted Green Primary School, Downview Primary School, Edward Bryant School, the Nyewood Church of England infant and junior schools, the Rose Green infant and junior schools, South Bersted Church of England Primary School, Southway Primary School, and St Mary's Catholic Primary School. On the secondary side, the alternatives to Felpham Community College are The Regis School in central Bognor and St Philip Howard Catholic School. Which one a Felpham family ends up at depends almost entirely on geography rather than preference, and the village's eastern position in the wider area pushes the default toward Felpham Community College first.
None of those schools come with an Ofsted grade attached on this brief. That is not the same thing as saying they are ungraded by the Inspectorate in general. It does mean that this page cannot rank them. If you need a ranking, the Ofsted website carries the current reports for every state school named here, and the local authority's admissions portal carries the year-by-year catchment cutoffs. Both are public.
The Felpham schools picture is workable, with a primary and a secondary inside the village and a wider Bognor ring for fall-back. The page rates it average for the lack of grade data rather than for any verdict on the schools themselves. If you need an Ofsted-ranked answer to which one to aim for, that is a different question. If you need to know where the school gate is, you have your answer.