Nitai of Tekoa brought challah portions from Beitar, but [the Sages] did not accept [it] from him. People from Alexandria brought their challah [portions] from Alexandria, but [the Sages] did not accept [them] from them. People from Mount Tze-voim brought their bikkurim before [the festival of] Shavuos, but [the Sages] did not accept [them] from them, because of what is written in the Torah (Exodus 23:16): And the festival of the harvest, the first fruits of your labors, which you sow in the field.

And these are given to any Kohen: charamim, firstborn [animals], redemption of a [firstborn] son, redemption of a firstborn donkey, the foreleg, jaws, and abomasum, the first of the fleece, oil [of terumah temei'ah] for burning, consecrated items [of] the Temple, and bikkurim; R' Yehudah forbids bikkurim. Bitter vetch of terumah, R' Akiva permits, but the Sages forbid.