20 Sivan is observed as a fast day by certain communities, due to the hundreds of thousands of Jews killed al kiddush Hashem in the Gezeiras Tach V'Tat (years 5408-5409, 1648-1649), the Chelminitzki massacres. There are special selichos said and Vayichal is read. These can be found in some siddurim, such as Siddur Tefila Yeshara, the Berdichiver Siddur.
The massacres of started in Nemirov, Ukraine, on 20 Sivan when they slaughtered the entire Jewish community, including the Rov, a great tzadik named Reb Yechiel Michel ben Reb Elazar HY"D, author of Shivrei Luchos. The Berdichiver Siddur says that is why this date was picked as a fast day and points out that 20 Sivan never falls out on Shabbos. After, the massacres spread out to other parts. This happened during the life of the Shach, Tosefos Yom Tov and many other great tzadikim. There were many other great tzadikim killed during the massacres, including Reb Shimshon Ostropolier (3 Av). Yesod Veshoresh Ha'avodah says one should think about the terrible torture and suffering these people went through and all the Torah that was not learnt because they were killed.
Hashem Yinkom Domom
It is the first yahrzeit of the fourth Modzitzer Rebbe, R' Yisroel Dan ben R' Shmuel Eliyahu Taub, author of Nachlas Dan. See Heichal HaNegina for more.
Also the yahrzeit of:
R' Elazar Flecklesh, author of Teshuva Me'Ahava
R' Chaim Mordechai Labaton (1869) Lived in Eretz Yisroel, he was the author of Nechach Hashulchan