Applying for British Citizenship, but overstayed in the past

[lemoneye]

Hello everyone,

My wife is a non-EU citizen married to me, an EU National which acquired British Citizenship last year. She has been granted settled status recently. However, she previously overstayed in the UK between 2018 and the beginning of 2020, which is the only negative factor in her immigration history.
She has been working full time in the last 5 years and wants to apply for British Citizenship also this year. Would her past overstay affect her application?
We also want her two children which are under 18 to apply for British Citizenship at the same time with her, as they have already settled status thru me as I am their step father.
Additionally, would a cover letter be necessary? If so, what format should it be in, and what details should it include? Also what documents would be needed to upload?

[contorted_svy]

Does she have anything else against her good character? Has she volunteered in the community or done similar things to show her character has changed since then?

What is the situation with the children (apologies for the invasive question)? Did you adopt them? If so (some other member will correct me if I am wrong) then the immigration status of the biological father won't matter and they can apply under Section 3(1) https://www.gov.uk/government/publicati ... accessible if the following applies, as you already have become a British citizen:

Children applying in line with their parents
Children applying in line with their parents We recognise that a number of children apply for registration under section 3(1) at the same time as their parents apply for naturalisation. Such children have usually been living in the UK with the parents and have completed a period of lawful residence.

You must normally register where:

one parent is a British citizen or about to become one through registration or naturalisation
the other parent (if involved in the child’s life) is a British citizen or settled in the UK
the child has been resident in the UK for the last 2 years - (if the child is under the age of 2 you can accept a shorter residence period, taking into account the age of the child)
the child is settled in the UK
where necessary both parents consent to the registration or any objections by the non-applying parent are ill founded
there is no reason to refuse on character grounds
If a child does not meet all of the above criteria, you must consider whether the child meets any of the other scenarios where we would normally register. If not, you must consider in line with the guidance registering exceptionally below.

[lemoneye]

She does not have anything else against her good character. She has been working full time in these last 5 years. No voluntary work. The children are living with us. Brought them from her country and I applied for them to the EU Scheme as they are my stepchildren. They received settled status thru me, as I haed settled status when they arrived in the UK. All 3 of them want to apply at the same time for the British Citizenship, as I understand there is no need for her to wait for 12 months after settled status as I am Both an EU and British Citizen?

[contorted_svy]

Did you legally adopt them?

[lemoneye]

No, they are my step children and have EU settled status thru me as a stepfather. They arrived in the UK in 2022. Their biological father gave his consent for them to live with me and my wife.

[contorted_svy]

I am not sure in this case whether they should follow their father's immigration status then.