On the use of so-called 'zero genitive', marked by a simple apostrophe in spelling ('), as opposed to the 's genitive, Quirk, Greenbaum, Leech and Svartvik specify in A Comprehensive grammar of the English Language (pp. 320 & 321) that:
In addition to its normal use with regular plurals such as boys', the 'zero genitive' is used to avoid repetitive or awkward combinations of sounds in the following cases:
(i) with Greek names of more than one syllable that end in -s, as in:
Euripides' /di:z/ plays, Xerxes' army, Socrates' wife
(ii) with many other names ending in /z/, where in speech zero is a variant of the regular /ɪz/ genitive. There is vacillation both in the pronunciation and in the spelling of these names, but most commonly the pronunciation is /ɪz/, and the spelling is an apostrophe only. (In the following examples, the minority form is given in parentheses.)
WRITTEN FORMS
Burns' (Burns's) poem
Dickens' (Dickens's) novels
Jones' (Jones's) car
SPOKEN FORMS
/ˈbɜ:nzɪz (bɜ:nz)/
/ˈdɪkɪnzɪz (ˈdɪkɪnz)/
/ˈdʒəunzɪz (dʒəunz)/
Names ending in other sibilants than /z/ have the regular /ɪz/ genitive: Ross's /ˈrɒsɪz/ theories. However, Jesus and Moses normally have the zero form of the spoken genitive, /ˈdʒi:zəs/ and /ˈməuzɪz/, and are written Jesus' and Moses' (as well as Jesus's and Moses's).
(iii) with fixed expression of the form for . . . sake, as in for goddness' sake, for conscience' sake, where the noun ends in /s/.
Fadnavis presumably does not end with a /z/ sound but with /s/, just like Ross in Quirk's example, and therefore should form its genitive with 's, giving Fadnavis's.