For this purpose we don't have Mantras but we do have Stotras.
From this page you can learn for example the Shiva Aparadha Kshamapana Stotram, which is asking for forgiveness from Lord Shiva for the faults the devotee might have committed.
Aadau karmaprasangaat, kalayati kalushham, maatrikukshau-sthitam
Vin-muutraa-medhya-madhye, kathayati nitaraam, jaatharo
Yadyadvai tatra duhkham, vyathayati nitaraam,
shakyate kena vaktum,
Kshantavyo me aparaadhah, Shiva Shiva Shiva bho Shrii Mahaadeva Shambho., 1
Due to the my previous birth karmas, I was born inside my mother’s
womb, And placed between urine, excreta and heat, everything was sere
unhappiness And burnt a lot by the heat of the digestive fire. And
possibly none can describe the sufferings that I underwent there,
And So O Shiva Shambho! Be pleased to pardon my fault, sins, Oh Mahadeva., 1
This is the 1st stanza of the Stotra which was authored by Adi Shankara. Each stanza ends with the same line which is highlighted above and it asks for forgiveness from Lord Shiva.
Few more stanzas are:
Vaardhakye chendriyaanaam, vigata-gati-matish-cha,
praudhahiinam cha diinamh,
Kshantavyo me aparaadhah, Shiva
Shiva Shiva bho Shrii Mahaadeva Shambho., 4
When I was passing through ripe old age, My five senses got weakened,
My wisdom lost its memory, My body got weakened, Due to god given sin,
sickness and pain never leaving it, and my mind started roaming
behind, Useless passions and desires, And so I did not think of thee
Parameshwara, And So O Shiva Shambho! Be pleased to pardon My fault,
sins, Oh Mahadeva., 4
No shakyam smaarta-karma, pratipada-gahana,
Shraute vaartaa katham, me
vichaaraih shravana-mananayoh, kim nididhyaasitavyam,
me aparaadhah, Shiva Shiva Shiva bho Shrii Mahaadeva Shambho., 5
Unable I am to observe the complex rules of Dharma daily, what to say
about to follow very well the rules of Veda as told by Brahmins? I do
not have trust in the Dharma and not able to think or understand them
by listening to Vedas and also unable to ponder and meditate upon you
and so what is the use of daily learning, And So O Shiva Shambho! Be
pleased to pardon my fault, sins, Oh Mahadeva., 5
The very last stanza of the Stotra asks for forgiveness for all possible sins that might have been committed by the devotee through his various sensory organs.
Kara-charana-kritam vaak,-kaaya-jam, karma-jam vaa,
Shravana-nayana-jam vaa, maanasam vaa-aparaadhama,
Vihitam-avihitam vaa, sarvam-etat-kshmasva,
karunaabdhe, shrii mahaadeva shambho., 14
Whatever faults or mistakes I have done so far with the help of my
hands, legs, speech and body, also due to my actions, also by seeing
and hearing or may be mentally or as per the injunctions of Veda, all
these Oh Lord Shiva who is all compassionate please forgive me. You
are the Lord of all deities and one who nature is to bless all., 14
So, like this Stotra, we have KshamaPana Stotras dedicated to various deities where the devotee asks for forgiveness for the faults committed.
For example, from this page you can read the Devi Kshamapana Stotra, which was authored by Adi Shankara too. The pattern of this Stotra is the same as that of the previous one, and here too the devotee asks the Mother Goddess for pardoning the mistakes that the devotee might have committed.
I am quoting the last two stanzas below:
जगदम्ब विचित्रमत्र किं परिपूर्णा करुणास्ति चेन्मयि ।
अपराधपरम्परापरं न हि माता समुपेक्षते सुतम् ॥११॥
Jagadamba Vicitram-Atra Kim Paripuurnnaa Karunnaa-[A]sti Cenmayi |
Aparaadha-Paramparaa-Param Na Hi Maataa Samupekssate Sutam ||11||
11.1: O Jagadamba (Mother of the Universe), What is surprising in this!
11.2: The graceful Compassion of the (Blissful) Mother always remains fully filled,
11.3: (Because) Inspite of the son committing Mistakes after Mistakes,
11.4: The Mother never abandons the son,
मत्समः पातकी नास्ति पापघ्नी त्वत्समा न हि ।
एवं ज्ञात्वा महादेवि
यथायोग्यं तथा कुरु ॥१२॥
Matsamah Paatakii Naasti Paapa-Ghnii Tvatsamaa Na Hi | Evam Jnyaatvaa
Mahaadevi Yathaa-Yogyam Tathaa Kuru ||12||
12.1: (O Mother) There is no one as Fallen like me, and there is no one as Uplifting ( by removing Sins ) like You,
12.2: Considering thus, O Mahadevi, Please do whatever is proper (to save me).
So, you can get such Stotras but probably not Mantras.
From here, you can learn the Tripura Saundari Aparadha Kshamapana Stotram:
Kunja manohara pada chalan Mani noopura hamsa virajithe,
bhavadhi surougha parishtutha loka visruthwara vaibhave,
vag maya nirjitha keera kale achala rajasya kannighe,
Lalitha parameshwari, Mam aparadhinam ambike., 1
Oh mother I have committed mistakes, so look after me Oh Lalitha
Parameshwari, Who with her pretty feet walks like a swan, With her gem
studded anklets making jingling sound, Who has the fame of creating
the world and being praised by Brahma and other devas, Who is filled
with pretty voice like that of a parrot and is the daughter of the
and from here, the Datta Aparadha Kshamapana Stotram.
1.Dathathreyam thwam namami praseedha,
Thwam sarvathma , sarva kartha na Veda,
Kopyantham they srava devaddhi deva,
Jnatha ajnathan may aparadhaan kshamaswa,
I salute Dathathreya to please him, For he is the soul and doer and ,
Is the God of Gods at the end of Vedas,
And he would pardon mistakes done knowingly or unknowingly.
All these Stotras are prayers requesting for forgiveness from the deity of your choice. So, reciting these Stotras is equivalent to asking for forgiveness.
So does really, chanting Mantra without Initiation, gives Bad result
or has opposite effect.
For this query see the answer here. Generally, Mantra chanting without initiation is considered as a sin and if done it may have negative effects.
Kalpe drishtA tu yo mantram japed gurumanAsritaha |
bhavet tasya phalam kinchinna vidyate ||
The person who, without depending on a Guru (Gurumanasitaha), chants
mantras by taking them from a book, gets his progeny destroyed [by
doing so] (sutanasho) and does not get any benefits [of the chant]
So, it is definitely not a recommended act.