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Line breeding is the only method by which you get consistant results. If you like what you have then breed that trio, take pullets from that mating back under the cock bird, and a cockrell back over those hens.
The birds pictured appear to be Millie Fluer with runaway white.. that will be no problem to continue to duplicate. Do not bring in any new birds.
Lets assign "names" here. Cock bird C1, Hens H1, Offspring cockrells c2. and pullets h2.
Year 1 C1xH1=c2,h2
Your next matings are
Year 2 C1xh2 Pen 1 and c2xH1 Pen 2
Year 3
C1xh2 Pen 1
c2xH1 Pen 2
Take cockrells from C1xh2 and mate to pullets from c2xH1. this is Pen 3
take Pullets from C1xh2 and a cockrell from c2xH1 this is pen 4
Now you have an established family with 4 breed pens, You can expand teh pens up to what ever makes you happy. Just select and cull. Do not bring in any "New Blood" as you will have the birds closely related close enough with teh same selection process on your yard and yet not so closely related that it will cause you a problem. Rotate breeder males every 5 years, and females every 3-4 years. You can maintain the line a very long time.