It is very common to place a cleavable sequence at the N-terminus to assist with purification of overexpressed proteins, such as His tags, FLAG tags, etc. The tags can later be removed by treatment with a proteolytic enzyme specific for it, such as TEV or thrombin. Expression vectors for these tagging strategies, and the cleaving enzymes, are commercially available.

Thanks Dr. Adam B Shapiro for your reply,

But I need the protein to be processed in vivo (i.e the proteolytic cleaving occurs by intracellular enzymes).

N-terminal secretion signals, such as pelB which signals transport out of the cytoplasm, are processed in vivo by signal peptidases.

https://en.wikipedia.org/wiki/PelB_leader_sequence

I agree with Adam B Shapiro. Moreover, different signal peptides should be selected according to the source of the target gene and the expression systems.

In the prokaryotic expression system, the signal peptides of E. coli are different from those of Bacillus subtilis in protein localization. Bacillus subtilis can secrete a large number of extracellular proteins, so it is a good system to study protein expression and secretion. In the yeast expression system, it is necessary to use the signal peptide of the yeast itself to guide the expression of heterologous proteins in order to avoid the wrong cleavage or incomplete cleavage of the signal peptide.

https://microbialcellfactories.biomedcentral.com/articles/10.1186/s12934-018-0901-3

in E.coli Methionine aminopeptidase (MetAP) catalyzes the hydrolytic cleavage of the N-terminal methionine from newly synthesized polypeptides. so you won't have a methionine at the start of the protein anyway.

if you need an N-terminal tag just use a sumo-tag and sumo protease.

Thanks all for reply,

Using a signal peptide will lead the protein of interest to the secretory pathway resulting ultimately in an extracellular protein. I agree with Trevor Huyton .