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Haskell, 120 84 7473 bytes

f x=[r|x=do(v,u)<-zip['a'..'z']['A'..],];1:r<-[sum[1|k<[[1|k<-x,v==k||u==k]],r>0]>>=showv==k||u==k]];show$sum$1:r

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-36 bytes thanks to Unrelated String

-1011 bytes thanks to Wheat Wizard

Haskell, 120 84 74 bytes

f x=[r|(v,u)<-zip['a'..'z']['A'..],r<-[sum[1|k<-x,v==k||u==k]],r>0]>>=show

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-36 bytes thanks to Unrelated String

-10 bytes thanks to Wheat Wizard

Haskell, 120 84 73 bytes

f x=do(v,u)<-zip['a'..'z']['A'..];1:r<-[[1|k<-x,v==k||u==k]];show$sum$1:r

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-36 bytes thanks to Unrelated String

-11 bytes thanks to Wheat Wizard

deleted 24 characters in body
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Haskell, 120 8484 74 bytes

import Data.Char
f i=filter(>0)[length.filterx=[r|(==nv,u)$toLower<$>i|n<<-['a'zip['a'..'z']]>>=show'z']['A'..],r<-[sum[1|k<-x,v==k||u==k]],r>0]>>=show

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-36 bytes thanks to Unrelated String

-10 bytes thanks to Wheat Wizard

Haskell, 120 84 bytes

import Data.Char
f i=filter(>0)[length.filter(==n)$toLower<$>i|n<-['a'..'z']]>>=show

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-36 bytes thanks to Unrelated String

Haskell, 120 84 74 bytes

f x=[r|(v,u)<-zip['a'..'z']['A'..],r<-[sum[1|k<-x,v==k||u==k]],r>0]>>=show

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-36 bytes thanks to Unrelated String

-10 bytes thanks to Wheat Wizard

added 18 characters in body
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Haskell, 120120 84 bytes

import Data.Char
c l n=length$filter(==n)l
g []=""
gf i=filter(i:r>0)|i==0=g r|1>0=show i++g r
f i=g$map[length.filter(c$map toLower i==n)$toLower<$>i|n<-['a'..'z']'z']]>>=show

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-36 bytes thanks to Unrelated String

Haskell, 120 bytes

import Data.Char
c l n=length$filter(==n)l
g []=""
g (i:r)|i==0=g r|1>0=show i++g r
f i=g$map(c$map toLower i)['a'..'z']

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Haskell, 120 84 bytes

import Data.Char
f i=filter(>0)[length.filter(==n)$toLower<$>i|n<-['a'..'z']]>>=show

Try it Online!

-36 bytes thanks to Unrelated String

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