JAPANESE ONLY The article below is based on non-localized content only available in Japanese. As such, all information in this article is based on fan-contributed translations.
Zansakura -zanka- (残桜 -zanka- lit. Remaining Cherry Blossoms -zanka-) is a character song performed by Megumi Ogata as Nagito Komaeda.
It was released on August 3rd, 2016 as a B-side single alongside Zettai Kibō Birthday. There is also a karaoke version. According to Ogata, Zansakura -zanka- is how Nagito feels on the inside, while the other song is how he feels outside. 
The lyrics appear to be Nagito's metaphorical descriptions of his own life and thoughts, with him being a withering, broken branch which is left behind alone. The song describes short-lived cherry blossoms, which are an enduring metaphor for mortality and the ephemeral nature of life in Japan. The Japanese also reckon the cherry blossom is the most beautiful not when it is in full bloom, but when it starts to wither and fall.
Interestingly, Nagito keeps mentioning ordinary life, which he claims to dislike. In Super Danganronpa 2.5: Nagito Komaeda and the Destroyer of the World, it is indeed confirmed that he wishes to live ordinary life, as his imaginary world reflects this desire and one of the many possible outcomes his life could have taken. However, he denies this.
「明日もまた会えるね」と 笑ってた心の 徒桜(あだざくら)
"asu wo mata aerune" to waratteta kokoro no ada zakura
"We can see again tomorrow", I laughed, short-lived cherry blossoms within my heart
花霞 煙りたつ彩(いろ) 誘(いざな)われ 辿りついたら
hana kasumi kemuri tatsu iro izana ware tadoritsuitara
the mist of flowers, tempted by the color of smoke rising, reach destination after a struggle
花影は 水の紋に 揺れて堕ちた
hanakage wa mizu no mon ni yurete ochita
shadow of the flower on the ripples in the water, shuddering and falling below
温もりを 伝えあうように 開く 桜(はな)のように
nukumori wo tsutaeau yō ni hiraku hana no yō ni
cherry blooms, as if to tell about the warmth
heibon ni saite chiriyuku michi wa
the life which blooms and withers in ordinariness
doko ni ochiterudarō
where would it fall?
刻まれる 針 止まる 満開の心に 桜雨(さくらあめ)
kizama reru hari tomaru mankai no kokoro ni sakura ame (sakura ame)
time comes around and the clock's hand stops, the heart blooms fully, the rain of cherry blossoms
花嵐 突然の風 立ち止まり 瞳(め)を開いたら
hanārashi totsuzen no kaze tachidomari me wo hiraitara
the storm of flowers, the sudden wind, I halt and open my eyes
花筏 水面覆い 流れ去った
hana ikada minamo ōi nagare satta
the flower rafts cover the water's surface, flowing away
ゆく春を 惜しみあうように 開く 桜(はな)のように
yuku haru wo oshimiau yō ni hiraku hana no yō ni
cherry blooms, as if to cherish the departing spring
heibon ni ikite tomoni yuku koto
to live an ordinary life, and die together with you
kanau nonaraba aah…
oh, if that could come true
北風と太陽が 皆 平等に降り注ぐものなら
kitakaze to taiyō ga mina byōdō ni furisosogu mononara
if the northern wind and the sun treat everyone equally
arashi wo norikoeta saki ni kibō ga saku to...
when a giant flower (hope) will bloom after surviving the storm
気がつけば 枯れゆく枝に ひとり 残されてた
kigatsukeba kareyuku eda ni hitori nokosareteta
at the moment I realized, the withering branch had been left behind all alone
手折られて 朽ちゆく傷が 渇きゆくまま
taorarete kuchiyuku kizu ga kawakiyuku mama
have been broken, wounds decaying, still keeping on yearning
来る冬を 迎え撃つように 開く 桜(はな)のために
kuru fuyu wo mukaeutsu yō ni hiraku hana no tame ni
cherry blooms, as if to fight the approaching winter
heibon nai nochi sosogeru hi made
until the day this ordinary life is devoted
continue blooming on like crazy
The "flower raft" (花筏) is a term Japanese poets used to describe cherry blossoms densely scattered on the surface of the river water.
In the song, Nagito describes himself as a broken branch. The word "branch" (枝) in the song is the same word as "eda" (枝) in his last name.