I notice that when referring to God in the second person in a possessive form, Sefardim often use the female form where Ashkenazim use the male form.
For example, where Ashkenazim say in kedusha, "כַּכָּתוּב עַל יַד נְבִיאֶךָ", Sefardim say "וְכֵן כָּתוּב עַל יַד נְבִיאָךְ". Notice the difference in the last word.
Another example: In birchas hamazon Ashkenazim say "רַחֶם נָא יי אֱלהֵינוּ עַל יִשְׂרָאֵל עַמֶּךָ. וְעַל יְרוּשָׁלַיִם עִירֶךָ. וְעַל צִיּוֹן מִשְׁכַּן כְּבוֹדֶךָ", while Sefardim say "רַחֵם יי אֱלֹהֵינוּ עָלֵינוּ וְעַל יִשְׂרָאֵל עַמָּךְ. וְעַל יְרוּשָׁלַיִם עִירָךְ. וְעַל הַר צִיּוֹן מִשְׁכַּן כְּבוֹדָךְ" Again, notice the "ךְ" ending instead of the "ךָ".
Although, there are those instances where even Ashkenazim use the female form. (e.g. מודִים אֲנַחְנוּ לָךְ.) But in my limited study of Tanach, I seem to recall God as always being referred to in the male form.
What is the reason for this difference between Ashkenazic and Sefardic liturgy, and its origin?