Global or local alignment on sequences for which it is assumed that they have common ancestry As the title says I would like to know which alignment method(global or local) should I use for sequences for which is assumed that they have common ancestry?

The sequences are 21 aa long peptide chains (proteins).

About the background of the sequences, it's only stated that it's ASSUMED that they are from the same ancestry.

The thing that we assume that they are from the same ancestry makes me confused. I know that on similar sequences with the same length usually, we use global.
My initial reaction is that 21 amino acids is too little information to demonstrate these proteins are homologues (which is the question behind your question). A homologous site means it shares a common ancestry and is distinguishable from random chance or convergent evolution. A common ancestor can be demonstrated using phylogeny (trees).

If a regular alignment program cannot align these sequences, such as clustalo or muscle, the assumption they are homologues cannot be easily tested using phylogeny. That would then become complicated at which point you would need to ask whether it is worth pursing the question.

My recommendation is to perform a simple protein-protein blast and assess the e-scores to get some feel about you data. Your question is achievable, but you would solve this in context to additional sequence data. Whether that sequence data is a denser sample or else contiguous sequence data needs further exploration.