Gemara

Rosh Hashanah 12b - Rav Asi - Question: "Mi'Ketz Sheva Shanim b'Mo'ed Shenas ha'Shemitah b'Chag ha'Sukos" - this is in the eighth year. Why is it called Shemitah?

Answer: This teaches that any Tevu'ah that was a third grown before Rosh Hashanah has Kedushas Shemitah.

13b - Mishnah: If rice, millet, poppy or sesame took root before Rosh Hashanah, it is tithed like the previous year's produce, and (if the coming year is Shemitah) it is permitted in Shemitah;

If not, it is forbidden in Shemitah (if the coming year is Shemitah), and (if not) it is tithed like the coming year's produce.

Question (Rabah): Chachamim said that we follow Chanatah regarding trees, a third growth regarding Tevu'ah, and Lekitah (when it was picked) regarding Yerakos (vegetables planted in order to eat the growth, not the seeds). Like which of these do Chachamim consider rice, millet...?

Answer (Rabah): Since they are picked a bit at a time, Chachamim follow Hashrashah (when it took root), lest one tithe from old on new or vice-versa).

Shmuel (For Ma'aser) we follow the final produce.

Sukah 39a - (Mishnah): One who buys a Lulav from his friend in Shemitah, the seller gives the Esrog for a gift, because one may not buy it in Shemitah.

Gemara: The case is, the seller is an Am ha'Aretz. The buyer pays extra for the Lulav (so the seller will give the Esrog for free), because it is forbidden to give Demei Peros Shemitah to an Am ha'Aretz.

39b - Question: The same concern should apply to giving money to the Am ha'Aretz for the Lulav!

Answer: The Lulav was detached (early) in the seventh year (before Sukos, so surely Chanatah was before Rosh Hashanah, so) it is considered sixth year.

Question: The same should apply to the Esrog!

Answer: The status of an Esrog depends on Lekitah (and it was in Shemitah).

Tana'im argue about whether the status of an Esrog depends on Lekitah or on Chanatah.

Toras Kohanim (Behar Perek 1:4): "Shenas Shabason Yihyeh la'Aretz" - Melachah is permitted immediately after Shemitah, but the fruits are forbidden until Tu bi'Shvat.

Gra: This is the correct text. The Tana justifies why it says "Shenas", for the Isur Melachah is only one year, even though the Isur Peros continues longer.:

Rishonim

Rambam (Hilchos Shemitah v'Yovel 4:9): Tishrei 1 is Rosh Hashanah for Shemitah and Yovel. If sixth year produce entered the Shemitah year:

Regarding Tevu'ah, legumes or fruits, if they reached Onas Ma'aser (sufficient development to obligate tithing) before Rosh Hashanah they are permitted. Even if they are gathered in Shemitah, they are like sixth year produce in every respect;

If they reached Onas Ma'aser after Rosh Hashanah they are like Shemitah produce.

Kesef Mishneh: Rav Asi expounded "Mi'Ketz Sheva Shanim..." to teach about seventh year produce that entered the eighth year. The same applies to sixth year produce that entered Shemitah.

Rambam (11): For Mitzri bean planted for seeds, rice, millet, poppy or sesame, if it took root before Rosh Hashanah, we follow the full development. If it was finished before Rosh Hashanah it is permitted in Shemitah like sixth year produce. If it was finished after Rosh Hashanah, even though it took root before Rosh Hashanah, it is forbidden like Sefichim of Shevi'is.

Question: A Mishnah says that we follow Hashrashah!

Answer #1 (Radvaz): We do not follow that Mishnah. Regarding Ma'aser mid'Rabanan, Chachamim made up several times. They cannot do so regarding Shemitah mid'Oraisa!

Answer #2 (Radvaz and Kesef Mishneh): Shmuel taught that we follow the full development (regarding Ma'aser), unlike the Mishnah. The Rambam understands that this applies to Shemitah also.

Question (Tosfos 13b DH Echad): R. Shimon Shezuri follows Hashrashah, and we do not find a Tana that argues. How can Shmuel argue?

Answer (Rashi DH Ishtamitsei): Shmuel follows a different Tana. I do not know who the Tana is.

Rambam (12): Regarding Yerek we follow when it was picked.

Source (Kesef Mishnef): The Gemara says that we follow when it was picked regarding Ma'aser. The Rambam understands that the same applies to Shemitah

Source (Ri Korkus): In Nedarim (57b) the Gemara discusses an onion uprooted in Shemitah and replanted in Sheminis. This connotes that regarding Yerek in Shemitah we follow when it was picked.

Tosfos (ibid.): The Gemara says that for Yerek we follow when it was picked. Really, it depends on full development. For Yerek these are the same. However, other things are picked long after full development.

Rambam (13): The same applies to seventh year produce that entered the eighth year. Regarding Tevu'ah, legumes or fruits, we follow Onas Ma'aser. Regarding rice, ...or Mitzri bean planted for seeds we follow the full development. Regarding Yerek we follow when it was picked.

Radvaz: This discusses when the produce is finished enough to be eaten. One may not eat Shemitah produce beforehand, for this is like wasting it.

Kesef Mishneh and Ri Korkus: This is how we determine whether it is considered Shemitah or eighth year produce.

R. Chananel (in Oz v'Hadar edition, 15b DH Shevi'is): If Chanatah was after Tu bi'Shvat of Shemitah, the fruits have Kedushas Shemitah.

Poskim

Shulchan Aruch (YD 331:126): Esrog is unique among fruits. It is like Yerek, and we follow when it was picked, both for Ma'aser and for Shemitah. Nevertheless, if a sixth year Esrog entered Shemitah, even if it was only a k'Zayis when Shemitah came, Ma'aser must be taken from it.

Taz (29): This is because regarding Shemitah we do not follow Chanatah.

Shach (146): Regarding Shemitah we follow Chanatah, like for other trees. Since this is not considered Shemitah because Chanatah was in Shishis, it is totally considered Shishis.

Tosfos R. Akiva Eiger (Rosh Hashanah [5]): Regarding Shevi'is of fruits we follow Chanatah, and Rosh Hashanah is Tishrei.

Question (Rashash Rosh Hashanah 2a DH Sham b'Echad): I did not find this explicit anywhere. The Rambam says that Tishrei is Rosh Hashanah, like R. Akiva Eiger. However, the Rambam also says that we follow Onas Ma'aser; this is very difficult.

Answer (Ri Korkus Ma'aser Sheni 1:1 DH Od Sham (13b)): The Rambam holds that Chanatah is Onas Ma'aser.

Chazon Ish (Shevi'is 7:13): It seems that even for trees, Shemitah is from Rosh Hashanah to Rosh Hashanah. The year is based on Tu bi'Shvat only for Ma'aser, which depends on when the fruits grow. But just like the Isur of plowing and planting in Shemitah is from Rosh Hashanah, also Kedushah of fruits depends on whether or not Chanatah was between Rosh Hashanah before Shemitah and Rosh Hashanah after Shemitah. Sukah 39b proves this. An Esrog picked between Rosh Hashanah and Sukos of Shemitah has Kedushas Shemitah because we follow picking. Regarding Ma'aser, before Tu bi'Shvat is considered last year's produce.