Which one of the following products was produced as a result of DNA manipulation in the first transgenic cow 'Rosie' ?

The correct option is α-lactalbumin.

Detailed Explanation:
In 1997, scientists produced the first transgenic cow, which they named 'Rosie'. Rosie was genetically modified through DNA manipulation to produce milk that was more nutritionally complete for human infants compared to natural bovine milk.

The modification involved introducing the human gene encoding the protein alpha-lactalbumin into the cow's genome. This allowed Rosie to produce milk containing human alpha-lactalbumin, which is a major whey protein in human breast milk but is typically present in very low amounts or absent in normal cow milk.

This protein is represented as:
$\alpha$-lactalbumin
Rosie's milk contained approximately 2.4 grams of this human protein per liter, making it a highly nutritious alternative for human babies who could not be breastfed.

Analysis of Other Options:
1. α-1-antitrypsin: This human protein is used in the treatment of emphysema and has been produced in other transgenic systems (such as transgenic sheep), but it was not the product engineered into Rosie.
2. β-lactglucose: This is not a standard protein or product associated with transgenic Rosie.
3. α-deaminase: This option does not represent the product of Rosie's genetic modification; it is likely a distractor name, possibly confusing the term with adenosine deaminase (ADA), which is famous in gene therapy history.