Dua Nudbah - Excerpt by Mahdi Samavati دعائے ندبہ

Over here, Imam (a.t.f.s.) has been addressed with the renowned title that finds a mention in the Holy Qur'an. “Surely the remnant (representative) of Allah is good for you if you are believers.” (Surah Hud - Verse 86)

The word بقية has several meanings. However, for clarity, we have delved only on one meaning which is relevant to our discussion over here.
بَقي مِنْهُ: تُرِكَ بَعْضُهُ
i.e. some of it’s part is left.
This means that Imam-e-Asr (a.t.f.s.) is the last link preserved by Allah in His chain of Prophets (a.s.) and their successors (a.s.) sent for mankind’s guidance.

This is also the meaning used in Ziyarat and supplications such as in Ziyarat e Aal Yasin:
اَلسَّلَامُ عَلَيْكَ يَا بَقِيَّةَ اللّٰهِ فِيْ اَرْضِهِ
‘Salutation upon the Remnant of Allah, from His Friends and His Proofs.’

بقيةُ الله
was the title of even the previous Imams (a.s.). However, it is used more specifically for Imam-e-Asr (a.t.f.s.). The following tradition underscores this fact.

A denier of the Holy Quran approached Ameerul Momineen (a.s.) and asked him, ‘I have read in the Quran, ‘the Remnant of Allah is better for you.’ Who is this Remnant of Allah?
Imam (a.s.) informed, ‘This refers to the Mahdi, who shall reappear after a period of intense examination. He shall then fill the earth with justice and equity as it would have been
filled with tyranny and injustice. Among his signs are occultation and a concealed lifestyle. At that time, rebellion and upheavals will be common and the fire of vengeance will be stoking strongly among the people. (Behaarul Anwaar vol. 93, p. 115.)

When Imam Hasan Askari (a.s.) introduced Ahmed b. Ishaaq (r.a.) to Imam-e-Zamana (a.t.f.s.) while he was still an infant, Imam (a.t.f.s.) declared to Ahmed b. Ishaaq (r.a.):
انا بَقِيَّةَ اللّٰهِ فِيْ اَرْضِهِ

‘I am the Remnant of Allah on His earth.’
This is the very statement that Imam (a.t.f.s.) shall proclaim on his reappearance. Imam (a.t.f.s.) shall be sighted first in the precincts of the Holy Kabaa where while leaning against the sacred monument. Kabaa, he shall recite the above statement. (source: Ziyarat Aal-e-Yasin: A Brief Commentary)