There is an obligation to make Kiddush on Shabbat mornings before the Se’uda. The Gemara calls this Kiddush "Kiddusha Rabba"- the big Kiddush. This is a euphemism, for unlike the Kiddush said on Friday night that must have verses preceding it, for the Shabbat morning Kiddush it suffices to just say "Bore Peri Hagefen" with no verses preceding it. However, the custom is to recite many Pessukim before this Kiddush such as, "Mizmor Le’david Hashem Ro’ee Lo I’Hsar", "Im Tashib", and "Veshameru".
The Mishna Berura (Rabbi Yisrael Meir Kagen Ha’kohen, 1839-1933) writes that it is improper to recite the Passuk of "Al Cen Be’rach Hashem Et Yom Ha’shabbat Vay’kadeshe’hu" in the Kiddush. The reason is that the words "Al Cen Berach Hashem" etc. come from an end of a verse and it is forbidden to say half Pessukim. However, the custom is to follow the Arizal (Rabbi Yis’hak Luria, 1534-1572) who writes that it is proper to say this Passuk in the Kiddush. The Ben Ish Hai (Rabbi Yosef Haim, Baghdad, 1833-1909) explains the Arizal (Rav Pealim Helek 1, 11) that since there is an "Atnah’" (cantillation note) before the words "Al Cen Berach Hashem", it is considered a verse on its own.
Hacham Ben Sion Abba Shaul (Isreal,1923-1998) writes(Ohr Le’sion Helek 2) that it is proper and very positive to say the words "Yom Ha’shishsi" in the Friday night Kiddush. Seemingly, this poses a problem, for it is only part of a Passuk. He writes that it is possible that only saying two words from a verse is not an issue. He continues to reason that since there are opinions that hold that it is only forbidden to say part of a verse if it is being read from the Torah, so in this case it is permissible.
Summary: There is an obligation to make Kiddush on Shabbat mornings before the Se’uda. It is proper to precede the Kiddush with the Passuk of "Al Cen Be’rach Hashem Et Yom Ha’shabbat Vay’kadeshe’hu". One should recite in the Friday night Kiddush the words "Yom Ha’shishi" for many secrets lie within them.
