I want to expand my English vocabulary. So, I need a dictionary or mobile app that can show me the relevant words grouped by their parts of speech. But I am not able to find anything like it after hours of searching. Do anything like this exists?
Oxford English Dictionary, a subscription resource, "Advanced Search" may do what you want. I'm unsure exactly what you're asking, but I expect that because you ask for "anything like this", my answer is an answer.
For example, I recently had occasion to find all pronouns in OED. At the "Advanced Search" I selected "Pronoun" from the "Part of speech" drop-down list, then clicked the "Search" button. That produced a list of the 285 entries for pronouns in the OED. The list can be sorted by entry (alphabetical), frequency, or date of first known (by OED) attestation of the entry (that is, not necessarily the pronoun) in English.
Setting other parameters of the advanced search may allow you to restrict the list to entries for words you consider "relevant".