||श्री कृष्णः शरणं मम||
||श्री कृष्णं शरणं मम||
||श्री कृष्णाय शरणं मम||
||श्री कृष्ण शरणं मम||
I see all these various forms online. Which one is correct grammatically?
Note that this question would be more suitable for Sanskrit Language site which is currently in definition phase.
There are 7 cases of Nouns called Vibhakti (विभक्ति). (Quoting useful information regarding this from one Sanskrit Grammar tutorial site:
The following are the 7 different cases of a noun.
- Case 1 - Nominative -> प्रथमा / prathamaa
- Case 2 - Accusative -> द्वितीया / dvitiiyaa
- Case 3 - Instrumental -> तृतीया / tRRitiiya
- Case 4 - Dative -> चतुर्थी / chaturthii
- Case 5 - Ablative -> पञचमी / paJNamii
- Case 6 - Genitive -> षष्ठी / ShaShThii
- Case 7 - Locative -> सप्तमी / saptamii
- Vocative -> सम्बोधन / sambodhana
श्री कृष्णः शरणं मम। means "Lord Krishna is my refuge" or "Shri Krishna is my shelter." (As already explained by Jonathan in the answer). Here Krishna is the subject/nominative in the sentence. Now let's see an example for the various forms of Sanskrit according to the case of Noun mentioned above:
(Here I'm quoting the forms of Sanskrit based on 7 cases of noun in tabular form for a boy बाल):
You may also refer Wikipedia page on Sanskrit Grammar which provides forms fro Rama (राम).
So, the grammatically correct Saranagati Mantra is:
॥श्री कृष्णः शरणं मम॥
श्री कृष्णः = Shri KRshNa: (subject case).
मम = mine (possessive case)
शरणं = protection/refuge (object case)
शरणं मम = my refuge.
So this roughly translates KRshna: is my refuge. Since this is in Sholka "अस्ति" is omitted.
Ideally, if prose, it would read "श्री कृष्णः मम शरणं अस्ति |"