The Obligation of Sending Prayers on the Prophet (sallallaahu 'alaihi wa sallam) in this Tashahhud:

Once, "he (sallallaahu 'alaihi wa sallam) heard a man supplicating in his prayer without glorifying the majesty of Allaah Exalted, nor sending prayers on the Prophet (sallallaahu 'alaihi wa sallam), so he said: This man has been hasty." He then called him and said to him and others, "When one of you prays, he should begin with the praise of his Lord, Sublime and Mighty, and his exultation, and then send prayers (in one narration: he should send prayers) on the Prophet (sallallaahu 'alaihi wa sallam), and then supplicate as he wishes." (255)

Also, "he heard a man glorifying and praising Allaah, and sending prayers on the Prophet (sallallaahu 'alaihi wa sallam) in prayer, so the Messenger of Allaah (sallallaahu 'alaihi wasallam) said to him: Supplicate, and you will be answered; ask, and you will be given." (256)

He (sallallaahu 'alaihi wa sallam) used to say, "When one of you has finished the [last] tashahhud, he should seek refuge with Allaah from four things:

[saying: O Allaah! I truly seek refuge with You]

1. from the punishment of Hellfire, and
2. from the punishment of the grave, and
3. from the trials of living and dying, and
4. from the evil [trials] of the False Christ.

[Then he should supplicate for himself with what occurs to him.]" (257) -"He (sallallaahu 'alaihi wa sallam) would supplicate with it in his own tashahhud." (258)

Also, "he used to teach the Companions (radi Allaahu 'anhum) this the way he taught them Soorahs of the Qur'aan." (259)

The Prophet (sallallaahu 'alaihi wa sallam) used to use different supplications in his prayer (260), supplicating with different ones at different times; he also endorsed other supplications, and "ordered the worshipper to select of them what he wishes." (261) They are:

1. "O Allaah! truly I seek refuge with You from the punishment of the grave, and I seek refuge with you from the trials of the False Christ, and I seek refuge with You from the trials of living and dying. O Allaah! truly I seek refuge with You from sin (262) and burden. (263)" (264)
2. "O Allaah! truly I seek refuge with You from the evil of what I have done, and from the evil of what I have not done (265) [yet]. (266)
3. "O Allaah! call me to account with an easy reckoning." (267)
4. "O Allaah! [I ask you], by Your knowledge of the Unseen, and Your control over the creation: give me life as long as You know that life is best for me, and take me when death is best for me. O Allaah! I also ask of You fear of You, in secret and in open; I ask of You the word of Truth (in one narration: Wisdom) and justice in anger and in pleasure; I ask of You moderation in poverty and affluence; I ask of You joy which does not fade; I ask of You pleasure [which does not pass away, nor that] which ceases; I ask of You contentment with Your decree; I ask of You coolness of life after death; I ask of You the delight of looking towards Your Face; and [I ask of You] eagerness towards meeting You, not in harmful adversity, nor in misleading afflictions. O Allaah! adorn us with thedecoration of eemaan, and make us those who guide and are guided.” (268)
5. He taught Abu Bakr as-Siddeeq (radi Allaahu 'anhu) to say: "O Allaah! indeed I have wronged myself greatly, and none can forgive sins except You, so forgive me out of Your forgiveness, and have mercy on me. Truly, You are the Oft- Forgiving, the Most Merciful." (269)
6. He instructed 'Aa'ishah (radi Allaahu 'anhaa) to say: "O Allaah! indeed I ask of You all Good, [the imminent and the far-off,] that of it which I know and that which I do not know. I seek refuge with You from all Evil, [the imminent and the far-off,] that of it which I know and that which I do not know. I ask of You (in one narration: O Allaah! indeed I ask of You) the Garden, and whatever saying or deed which brings one near to it; I seek refuge with You from the Fire, and (from) whatever saying or deed which brings one near to it. I ask of You (in one narration: O Allaah! indeed I ask of You) [the] good of what was asked of You by Your slave and messenger [Muhammad; and I seek refuge with You from evil of what Your slave and messenger Muhammad (sallallaahu 'alaihi wa sallam) sought refuge with You]. [I ask of You] that whatever You have decreed for me, its result [for me] be beneficial. (270)
7. He said to a man, What do you say during the prayer? He replied, "I bear witness (i.e. do the tashahhud), then I ask Allaah for the Garden, and I seek refuge with Him from the Fire. However, by Allaah, there is no murmuring (271) as good as yours or that of Mu'aadh." So he said, Our murmuring is like yours. (272)
8. He heard a man saying in his tashahhud: "O Allaah! indeed I ask of You, O Allaah (in one narration: by Allaah), the One, the Only, the Absolute, Who begets not and nor is He begotten, and there is none like Him, that You forgive me my sins; indeed You are the Oft-Forgiving, Most Merciful. On this, he (sallallaahu 'alaihi wa sallam) said, He has been forgiven, he has been forgiven.” (273)
9. He heard another man say in his tashahhud: "O Allaah! Indeed, I ask of You, by the fact that to You belongs all Praise; there is no(true) god except You, [You alone, You have no partners;] the Bestower of Favours; [O] Originator of the Heavens and the Earth; O One that is Full of Majesty and Honour; O Living One, O Eternal One; [indeed I ask of You] [the Garden, and I seek refuge with You from the Fire][So the Prophet (sallallaahu 'alaihi wa sallam) said to his Companions, Do you know with what he has supplicated? They said, "Allaah and His Messenger know best." He said, By Him in Whose Hand is my soul,] he has supplicated Allaah with His Mighty (in one narration: Mightiest) name (274), with which if He is supplicated, He answers, and with which if He is asked, He gives. (27
10. One of the last things he would say between the tashahhud and the tasleem would be: "O Allaah! Forgive me what I have done in the past, and what I will do in the future, and what I have concealed, and what I have done openly, and what I have exceeded in, whatever You know about more know than I. You are the Bringer-Forward, and You are the Delayer, there is no (true) god except You." (276)