In Middle English the word was cedule, from Old French, and it began with a plain S sound. Later the spelling was changed to sch, to match the Latin schedula. Once the new spelling was in place, speakers began to say what they saw.
They read sch in two ways. British English settled mainly on SH. American English chose SK, the sound of sch in school and scheme. Cambridge and Oxford both give SK for the US and SH for the UK.
The middle varies too. Oxford lists SHED-yool for British English and Cambridge lists SHEJ-ool; both are correct. Use the start that matches the accent you are learning. Speakers of either accent will understand you.