Is there any chance he could have changed his name? and this Bernie becomes Ernie? This is the only son I find with parents Paul and Mary in Erie, PA.
1910 United States Federal Census about Bernard Zdonski
Name: Bernard Zdonski [Bernard Zdowski]
Age in 1910: 4
Estimated birth year: abt 1906
Birthplace: Pennsylvania
Relation to Head of House: Son
Father's name: Paul Zdonski
Father's Birth Place: Germany
Mother's name: Mary Zdonski
Mother's Birth Place: Germany
Home in 1910: Erie Ward 2, Erie, Pennsylvania
Marital Status: Single
Race: White
Gender: Male
Household Members: Name Age
Paul Zdonski 49 married once 26 years, b. Germany/Polish, parents same, immig. 1888, papers filed, laborer at foundry,
Mary Zdonski 44 married once 26 years, 15 births, 5 living, b. Germany/Polish, parents same, no immig. year listed,
Veronica Zdonski 15 daughter, single, b. PA, parents b. Germany/Polish,
Joseph Zdonski 11 son, b. PA, parents b. Germany/Polish,
Hellen Zdonski 8 daughter, b. PA, parents b. Germany/Polish,
Bernard Zdonski 4 son, b. PA, parents b. Germany/Polish,
Source Citation: Year: 1910; Census Place: Erie Ward 2, Erie, Pennsylvania; Roll: T624_1342; Page: 6A; Enumeration District: 73; Image: 236.
429 E. 18th Street

Let me know if you want the 1920:
1920 United States Federal Census about Bernard Zdunsa
Name: Bernard Zdunsa[Bernard Zauncks] [Bernard Zdunska]
Home in 1920: Erie Ward 2, Erie, Pennsylvania
Age: 14
Estimated birth year: abt 1906
Birthplace: Pennsylvania
Relation to Head of House: Son
Father's Birth Place: Poland
Mother's name: Mary Zdunsa
Mother's Birth Place: Poland
Marital Status: Single
Race: White
Sex: Male
Able to read: Yes
Able to Write: Yes
Household Members: Name Age
Mary Zdunsa 55
Joseph Zdunsa 21
Helen Zdunsa 18
Bernard Zdunsa 14
Source Citation: Year: 1920;Census Place: Erie Ward 2, Erie, Pennsylvania; Roll: T625_1565; Page: 7B; Enumeration District: 76; Image: 169.