-「我が（わが）」：old Japanese - 「私の」：modern Japanese if you use 「我が」, it sounds grave, imortant, or making you look important (=偉そう） OK: 我が祖国：my country NG：我がペン: my pen OK：私の祖国 OK：私のペン

「我」(われ) is another word for "I" in Japanese. 「我が」 simply means "I," where が shows "I" is the subject. 「私」 also means "I." However, since it has の attached, it indicates the possessive, changing "I" to "my." 私の本 = "my book" Let's look at the particles again with each pronoun: が indicates the subject, so whether it is 「我が」or 「私が」, they both mean "I." For example: 我が日本人です。 - "I am a Japanese person." 私が日本人です。 - "I am a Japanese person." の indicates possession, so whether it is 「我の」 or 「私の」, they both mean "my." For example: これは私のペンです。- "This is my pen." これは我のペンです。- "This is my pen." Now, there is a distinct difference between 我 and 私 though. In conversation, you would almost never, ever say 我. 我 is much more formal and poetic. You mostly see it written, or perhaps in speeches or literature. I can almost guarantee you will never hear it in daily conversation, unless used jokingly. 私 is the more generally used pronoun for "I." You can use it with anyone, regardless of age or rank in relationship to you. This is what you will hear most often, as well as see it written. Sorry for the long explanation, I just wanted to explain it clearly. I hope this helps. If you have any further questions, please let me know.

To start let me say that the meaning of all of these sentences is the same. They are all telling you who the thing belongs to, the only difference is what you are emphasizing. When you use "my" it puts greater emphasis on the object. When you use mine it puts greater emphasis on who the object belongs to. How to use them correctly is defined below: Mine is a pronoun whereas my is an adjective; to be more specific, mine is a possessive pronoun, whereas my is a possessive adjective. So the word mine is used in reference to a noun, and my is used to describe a noun. For example: This is my house. My is describing the house, who it belongs to. The object after the word "my" is what matters. You are simply clarifying to someone that it is yours. This house is mine. Mine is referencing the house, also who it belongs to. The object is not as important here, but whose it is matters greatly. You are telling someone with emphasis that the house belongs to you. Side note (This may or may not be helpful) The part that is confusing about this is that the other possessive pronouns and possessive adjectives used in English are the same for other subjects. If I'm talking about you instead of me the examples would be: This is your house This house is yours. or This is his house. This house is his. or This is their house. This house is theirs. or This is our house. This house is ours.

私の、我が、both mean my not mine nor I. I recommend native Japanese Aki 's answer.