Could someone suggest me a project for bioinformatics that relates to phylogenetic analysis?
If you are talking about a thesis proposal, there are lots of researches related with mitochondrial analysis. Remember that mitochondrial was said to have evolved from proteobacterium (and chloroplast from cyanobacteria) during the endosymbiosis event approximately dated billions of years ago. Since the phylogenetic trees of the timeline of the evolution of mitochondria have already been sought, you can focus on any specific proteins that have evolved at any point during the early stages of the earth. Remember that cells evolve and complicate itself to form another types of organism during its evolution. If you are considering a project, a phylogenetic characterization of any ancestral protein that will show a distinction or relationships of organisms can be a good idea. For example, the protein characterization of rhodopsin (a protein which is present in humans which is also present in other organisms but slightly altered) is a great idea.